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%I #19 Mar 30 2012 17:22:57
%S 1,1,1,1,1,1,2,1,1,1,2,1,3,1,1,2,2,1,1,1,1,3,1,3,2,2,1,3,1,1,1,5,1,1,
%T 2,3,3,1,1,4,2,1,2,2,1,1,2,4,1,2,2,1,2,2,1,1,2,5,1,2,2,1,1,1,1,6,1,1,
%U 1,4,2,1,2,5,1,1,1,1,1,2,1,5,1,1,3,3,1,3,7,1,3,6,1,1,1,1,2,1,3,2
%N Number of times each value of the sigma function occurs.
%C The possible values of the sigma (sum of divisors) function are in A002191. Value A002191(n) occurs exactly a(n) times. Because sigma(x) >= x+1 (for x>1) with equality only at prime x, we know that for prime p, sigma(p) is the last time p+1 occurs as a value of sigma. This sequence is the same as A054973 without the zero terms.
%H T. D. Noe, <a href="/A185147/b185147.txt">Table of n, a(n) for n = 1..10000</a>
%t Transpose[Sort[Tally[DivisorSigma[1, Range[Prime[PrimePi[200]]]]]]][[2]]
%Y Cf. A007370 (numbers for which a(n)=1).
%K nonn
%O 1,7
%A _T. D. Noe_, Mar 18 2011