<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
<HTML><HEAD>
<META http-equiv=Content-Type content="text/html; charset=iso-8859-1">
<META content="MSHTML 6.00.2900.2722" name=GENERATOR>
<STYLE></STYLE>
</HEAD>
<BODY bgColor=#ffffff>
<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></BODY></HTML>