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

1,2

Links

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

Formula

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

Example

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.

Prog

(PARI) a(n)={n*sumdiv(n, d, vecprod(divisors(d))/d)} \\ Andrew Howroyd, Jan 05 2020
(Magma) [&+[&*Divisors(d)*(n div d):d in Divisors(n)]:n in [1..50]]; // Marius A. Burtea, 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

Crossrefs

Cf. A007955 (product of divisors), A322671.

Sequence in context: A154784 A328709 A062955 * A359103 A344223 A347263

Adjacent sequences: A174929 A174930 A174931 * A174933 A174934 A174935

Keyword

nonn

Author

Jaroslav Krizek, Apr 02 2010

Status

approved