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