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%I #7 Oct 31 2020 13:54:12
%S 0,0,1,0,2,0,3,0,0,0,4,0,5,0,0,0,6,0,7,0,0,0,8,0,1,1,0,0,9,0,10,0,1,0,
%T 1,0,11,1,0,0,12,0,13,0,0,0,14,0,1,0,1,0,15,0,1,0,0,0,16,0,17,0,0,0,0,
%U 0,18,0,0,0,19,0,20,1,0,1,1,0,21,0,2,0,22,0,1,1,1,0,23,0,2
%N Number of integers less than n with the same sum of proper divisors as n.
%F a(n) = |{j < n : sigma(j) - j = sigma(n) - n}|.
%e a(5) = 2 because A001065(5) = 1 and also A001065(2) = A001065(3) = 1.
%t Table[Length[Select[Range[n - 1], DivisorSigma[1, #] - # == DivisorSigma[1, n] - n &]], {n, 91}]
%o (PARI) a(n)={my(t=sigma(n)-n); sum(k=1, n-1, sigma(k)-k==t)} \\ _Andrew Howroyd_, Oct 31 2020
%Y Cf. A001065, A047983, A263025.
%K nonn
%O 1,5
%A _Ilya Gutkovskiy_, Oct 31 2020
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