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<DIV><FONT size=2>Note 1: The second %S in the modified sequence should be %U,
so the fixed sequence would be</FONT></DIV>
<DIV><FONT size=2></FONT> </DIV>
<DIV>
<DIV><FONT size=2>%I A072916</FONT></DIV>
<DIV><FONT size=2>%S A072916
3,8,19,41,117,254,616,1642,3766,9461,24183,60252,151368,385600,979844,</FONT></DIV>
<DIV><FONT size=2>%T A072916
2507393,6428977,16513542,42642649,110283280,285776799,742428731,<BR>%U A072916
1932223170,5038580446,13159683245,34423463648,90173540312</FONT></DIV>
<DIV><FONT size=2>%N A072916 Number of m such that Floor[Prime[m]/m] = n.<BR>%e
A072916 There are 8 values of m giving Floor[Prime[m]/m] = 2, namely m = m =
1,5,6,7,8,9,10,11, so a(2) = 8.</FONT><FONT size=2><BR>%t A072916 a(n_) :=
Length[Cases[Table[Floor[Prime[m]/m], {m, 1, 1000000}], n]]<BR>%K A072916
base,easy,nonn<BR>%O A072916 1,1</FONT><FONT size=2>.</FONT></DIV>
<DIV><FONT size=2>%e A072916 a(16) through a(27) from Farideh Firoozbakht Sep 13
2005<BR>%A A072916 Zakir F. Seidov (zakseidov(AT)yahoo.com) Aug 11
2002</FONT></DIV>
<DIV><FONT size=2></FONT> </DIV></DIV>
<DIV><FONT size=2>Note 2: The %t program as it stands is not sufficient to find
the larger extended values.</FONT></DIV>
<DIV><FONT size=2></FONT> </DIV>
<DIV><FONT size=2>Note 3: </FONT><FONT size=2>Once A072916 is fixed, A112547 may
be removed as a duplicate of it. A112547 is a very new sequence and
unlikely to have been referenced.</FONT></DIV>
<DIV><FONT face="Times New Roman" size=2></FONT> </DIV>
<DIV>----- Original Message ----- </DIV>
<BLOCKQUOTE dir=ltr
style="PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; BORDER-LEFT: #000000 2px solid; MARGIN-RIGHT: 0px">
<DIV
style="BACKGROUND: #e4e4e4; FONT: 10pt arial; font-color: black"><B>From:</B>
<A title=davidwwilson@comcast.net href="mailto:davidwwilson@comcast.net">David
Wilson</A> </DIV>
<DIV style="FONT: 10pt arial"><B>To:</B> <A title=seqfan@ext.jussieu.fr
href="mailto:seqfan@ext.jussieu.fr">Sequence Fans</A> </DIV>
<DIV style="FONT: 10pt arial"><B>Sent:</B> Saturday, September 17, 2005 2:55
AM</DIV>
<DIV style="FONT: 10pt arial"><B>Subject:</B> Proposed fix for A072916, plz
review</DIV>
<DIV><BR></DIV>
<DIV><FONT size=2>Currently A072916 looks like</FONT></DIV>
<DIV><FONT size=2></FONT> </DIV>
<DIV><FONT size=2>%I A072916<BR>%S A072916
3,7,19,41,117,254,616,1642,3766,9461,24183,60252,151368,385600,979844<BR>%N
A072916 Number of m such that Floor[Prime[m]/m] = n.<BR>%C A072916 First 12
primes are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37 First 12
Floor[Prime[m]/m]'s are: 2, 1, 1, 1\<BR> , 2, 2, 2, 2, 2, 2, 2, 3 Remove
first term and count ones, twos etc and get the sequence: 3,7,19...<BR>%e
A072916 a(2)=7, as seven primes 11, 13, 17, 19, 23, 29, 31 divided by their
order give numbers between 2 and 3.<BR>%t A072916 a(n_) :=
Length[Cases[Table[Floor[Prime[m]/m], {m, 2, 1000000}], n]]<BR>%Y A072916
Adjacent sequences: A072913 A072914 A072915 this_sequence A072917 A072918
A072919<BR>%Y A072916 Sequence in context: A077313 A049490 A047025
this_sequence A096447 A086519 A090689<BR>%K A072916 base,easy,nonn<BR>%O
A072916 1,1<BR>%A A072916 Zakir F. Seidov (zakseidov(AT)yahoo.com) Aug 11
2002</FONT></DIV>
<DIV><FONT size=2></FONT> </DIV>
<DIV><FONT size=2>According to the description </FONT><FONT size=2>a(n) counts
the number of m with Floor[Prime[m]/m] = n. The domain of Prime[m] is
set of positive integers, so the natural assumption would be that a(n)
counts positive m with Floor[Prime[m]/m] = n. </FONT><FONT
size=2>There are eight positive values of m satisfying </FONT><FONT
size=2>Floor[Prime[m]/m] = 2, namely, m = 1,5,6,7,8,9,10,11. We would
therefore expect a(2) = 8, however, for some inexplicable reason, m = 1 is
dropped from consideration (see "Remove first term" in comment) and so a(2) =
7 in the current sequence. Note that in the program given, m starts at 2
instead of 1 for no specified reason.</FONT></DIV>
<DIV><FONT size=2></FONT> </DIV>
<DIV><FONT size=2>My proposed version of this sequence counts m = 1 and
extends the sequence.</FONT></DIV>
<DIV><FONT size=2></FONT><FONT size=2></FONT> </DIV>
<DIV><FONT size=2>%I A072916</FONT></DIV>
<DIV><FONT size=2>%S A072916
3,8,19,41,117,254,616,1642,3766,9461,24183,60252,151368,385600,979844,</FONT></DIV>
<DIV><FONT size=2>%T A072916
2507393,6428977,16513542,42642649,110283280,285776799,742428731,<BR>%S A072916
1932223170,5038580446,13159683245,34423463648,90173540312</FONT></DIV>
<DIV><FONT size=2>%N A072916 Number of m such that Floor[Prime[m]/m] =
n.<BR>%e A072916 There are 8 values of m giving Floor[Prime[m]/m] = 2, namely
m = m = 1,5,6,7,8,9,10,11, so a(2) = 8.</FONT><FONT size=2><BR>%t A072916
a(n_) := Length[Cases[Table[Floor[Prime[m]/m], {m, 1, 1000000}], n]]<BR>%K
A072916 base,easy,nonn<BR>%O A072916 1,1</FONT><FONT size=2>.</FONT></DIV>
<DIV><FONT size=2>%e A072916 a(16) through a(27) from Farideh Firoozbakht Sep
13 2005<BR>%A A072916 Zakir F. Seidov (zakseidov(AT)yahoo.com) Aug 11
2002</FONT></DIV>
<DIV><FONT size=2></FONT> </DIV>
<DIV><FONT size=2></FONT> </DIV></BLOCKQUOTE></BODY></HTML>