Proposed fix for A072916, plz review

[David Wilson]

Currently A072916 looks like

%I A072916
%S A072916 3,7,19,41,117,254,616,1642,3766,9461,24183,60252,151368,385600,979844
%N A072916 Number of m such that Floor[Prime[m]/m] = n.
%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\
  , 2, 2, 2, 2, 2, 2, 2, 3 Remove first term and count ones, twos etc and get the sequence: 3,7,19...
%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.
%t A072916 a(n_) := Length[Cases[Table[Floor[Prime[m]/m], {m, 2, 1000000}], n]]
%Y A072916 Adjacent sequences: A072913 A072914 A072915 this_sequence A072917 A072918 A072919
%Y A072916 Sequence in context: A077313 A049490 A047025 this_sequence A096447 A086519 A090689
%K A072916 base,easy,nonn
%O A072916 1,1
%A A072916 Zakir F. Seidov (zakseidov(AT)yahoo.com) Aug 11 2002

According to the description 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.  There are eight positive values of m satisfying 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.

My proposed version of this sequence counts m = 1 and extends the sequence.

%I A072916
%S A072916 3,8,19,41,117,254,616,1642,3766,9461,24183,60252,151368,385600,979844,
%T A072916 2507393,6428977,16513542,42642649,110283280,285776799,742428731,
%S A072916 1932223170,5038580446,13159683245,34423463648,90173540312
%N A072916 Number of m such that Floor[Prime[m]/m] = n.
%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.
%t A072916 a(n_) := Length[Cases[Table[Floor[Prime[m]/m], {m, 1, 1000000}], n]]
%K A072916 base,easy,nonn
%O A072916 1,1.
%e A072916 a(16) through a(27) from Farideh Firoozbakht Sep 13 2005
%A A072916 Zakir F. Seidov (zakseidov(AT)yahoo.com) Aug 11 2002

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