A344996 a(n) = A048250(n) * A051709(n).

0, 0, 0, 3, 0, 24, 0, 9, 4, 36, 0, 96, 0, 48, 48, 21, 0, 108, 0, 180, 64, 72, 0, 240, 6, 84, 16, 288, 0, 1440, 0, 45, 96, 108, 96, 372, 0, 120, 112, 468, 0, 2304, 0, 576, 288, 144, 0, 528, 8, 234, 144, 756, 0, 360, 144, 768, 160, 180, 0, 4608, 0, 192, 448, 93, 168, 4608, 0, 1188, 192, 4032, 0, 900, 0, 228, 336, 1440, 192

Offset: 1

Author

Antti Karttunen, Jun 05 2021

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A048250, A051709.

Cf. also A344997.

Cf. A002117, A059956.

Programs

PARI

A048250(n) = factorback(apply(p -> p+1,factor(n)[,1]));
A051709(n) = ((sigma(n) + eulerphi(n)) - (2*n));
A344996(n) = (A048250(n)*A051709(n));

Formula

a(n) = A048250(n) * A051709(n).

a(n) = -[Sum_{d|n} mu(d)^2*d] * [Sum_{d|n, dA001065(d)].

a(n) = -Product(p_i + 1) * [Sum_{d|n, dA008683(n/d)*A001065(d)], where p_i are distinct primes dividing n.

Sum_{k=1..n} a(k) ~ c * n^3 / 3, where c = zeta(3) * Product_{p prime} (1 + 1/p^2 - 1/p^3) + 6/Pi^2 - 2 = 0.177775281124... . - Amiram Eldar, Dec 04 2023