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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.

%I A174932 #12 Sep 08 2022 08:45:51
%S A174932 1,4,6,16,10,54,14,96,45,130,22,1860,26,238,270,1216,34,6048,38,8300,
%T A174932 504,550,46,335688,175,754,864,22484,58,811050,62,35200,1188,1258,
%U A174932 1330,10095048,74,1558,1638,2576920,82,3113586,86,86372,92070,2254,94,255478416
%N 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.
%H A174932 Andrew Howroyd, <a href="/A174932/b174932.txt">Table of n, a(n) for n = 1..1000</a>
%F A174932 a(n) = n*A322671(n). - _Andrew Howroyd_, Jan 05 2020
%e A174932 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.
%o A174932 (PARI) a(n)={n*sumdiv(n, d, vecprod(divisors(d))/d)} \\ _Andrew Howroyd_, Jan 05 2020
%o A174932 (Magma) [&+[&*Divisors(d)*(n div d):d in Divisors(n)]:n in [1..50]]; // _Marius A. Burtea_, Jan 05 2020
%o A174932 (Python)
%o A174932 from math import isqrt
%o A174932 from sympy import divisor_count, divisors
%o A174932 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
%Y A174932 Cf. A007955 (product of divisors), A322671.
%K A174932 nonn
%O A174932 1,2
%A A174932 _Jaroslav Krizek_, Apr 02 2010