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

1,5

Links

Table of n, a(n) for n=1..91.

Formula

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A001065, A047983, A263025.

Sequence in context: A104117 A114511 A085199 * A085200 A080024 A348223

Adjacent sequences: A338501 A338502 A338503 * A338505 A338506 A338507

Keyword

nonn

Author

Ilya Gutkovskiy, Oct 31 2020

Status

approved