A380584 Number of positive integers <= n that have the same sum of odd divisors as n.

1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1, 5, 1, 2, 1, 3, 1, 2, 2, 4, 1, 2, 1, 3, 1, 3, 2, 6, 1, 2, 2, 3, 1, 2, 1, 4, 1, 3, 1, 3, 1, 4, 3, 5, 1, 2, 1, 3, 1, 2, 2, 4, 1, 2, 1, 5, 1, 4, 1, 7, 1, 4, 1, 3, 1, 5, 3, 4, 1, 2, 1, 3, 2, 2, 2, 5, 1, 2, 2, 5, 1, 2, 1, 4, 1, 2, 1, 6, 1, 6, 2, 6, 1, 2, 1, 3

Offset: 1

Author

Ilya Gutkovskiy, Jan 30 2025

Keywords

• nonn

Comments

Ordinal transform of A000593.

Links

• Eric Weisstein's World of Mathematics, Odd Divisor Function.

Crossrefs

Cf. A000593, A263025, A337557, A380653, A380654.

Programs

Mathematica

Table[Length[Select[Range[n], Sum[Mod[d, 2] d, {d, Divisors[#]}] == Sum[Mod[d, 2] d, {d, Divisors[n]}] &]], {n, 1, 100}]

Formula

a(n) = |{j <= n : A000593(j) = A000593(n)}|.