A338504 - OEIS

%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