A336563 - OEIS

A336563

Sum of proper divisors of n that are divisible by every prime that divides n.

0, 0, 0, 2, 0, 0, 0, 6, 3, 0, 0, 6, 0, 0, 0, 14, 0, 6, 0, 10, 0, 0, 0, 18, 5, 0, 12, 14, 0, 0, 0, 30, 0, 0, 0, 36, 0, 0, 0, 30, 0, 0, 0, 22, 15, 0, 0, 42, 7, 10, 0, 26, 0, 24, 0, 42, 0, 0, 0, 30, 0, 0, 21, 62, 0, 0, 0, 34, 0, 0, 0, 96, 0, 0, 15, 38, 0, 0, 0, 70, 39, 0, 0, 42, 0, 0, 0, 66, 0, 30, 0, 46, 0, 0, 0, 90

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OFFSET

1,4

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10800

Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

FORMULA

a(n) = A057723(n) - n.

a(n) = A007947(n) * A336567(n) = A007947(n) * A001065(A003557(n)).

a(n) = A336564(n) - A033879(n).

Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = A065487 - 1 = 0.231291... . - Amiram Eldar, Dec 07 2023

MATHEMATICA