A338504 Number of integers less than n with the same sum of proper divisors as n.

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, 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, 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

Offset: 1

Author

Ilya Gutkovskiy, Oct 31 2020

Keywords

• nonn

Examples

			a(5) = 2 because A001065(5) = 1 and also A001065(2) = A001065(3) = 1.
		

Crossrefs

Cf. A001065, A047983, A263025.

Programs

Mathematica

Table[Length[Select[Range[n - 1], DivisorSigma[1, #] - # == DivisorSigma[1, n] - n &]], {n, 91}]

PARI

a(n)={my(t=sigma(n)-n); sum(k=1, n-1, sigma(k)-k==t)} \\ Andrew Howroyd, Oct 31 2020

Formula

a(n) = |{j < n : sigma(j) - j = sigma(n) - n}|.