A174932 a(n) = Sum_{d|n} A007955(d) * A000027(n/d) = Sum_{d|n} A007955(d) * (n/d), where A007955(m) = product of divisors of m.

1, 4, 6, 16, 10, 54, 14, 96, 45, 130, 22, 1860, 26, 238, 270, 1216, 34, 6048, 38, 8300, 504, 550, 46, 335688, 175, 754, 864, 22484, 58, 811050, 62, 35200, 1188, 1258, 1330, 10095048, 74, 1558, 1638, 2576920, 82, 3113586, 86, 86372, 92070, 2254, 94, 255478416

Offset: 1

Author

Jaroslav Krizek, Apr 02 2010

Keywords

• nonn

Examples

			For n = 4, A007955(n) = b(n): a(4) = b(1)*(4/1) + b(2)*(4/2) + b(4)*(4/4) = 1*4 + 2*2 + 8*1 = 16.
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A007955 (product of divisors), A322671.

Programs

Magma

[&+[&*Divisors(d)*(n div d):d in Divisors(n)]:n in [1..50]]; // Marius A. Burtea, Jan 05 2020

PARI

a(n)={n*sumdiv(n, d, vecprod(divisors(d))/d)} \\ Andrew Howroyd, Jan 05 2020

Python

from math import isqrt
from sympy import divisor_count, divisors
def A174932(n): return n*sum(isqrt(d)**(c-2) if (c:=divisor_count(d)) & 1 else d**(c//2-1) for d in divisors(n,generator=True)) # Chai Wah Wu, Jun 25 2022

Formula

a(n) = n*A322671(n). - Andrew Howroyd, Jan 05 2020