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A174933 a(n) = Sum_{d|n} A007955(d) * A000027(d) = Sum_{d|n} A007955(d) * (d), where A007955(m) = product of divisors of m.

%I A174933 #12 Sep 08 2022 08:45:51
%S A174933 1,5,10,37,26,230,50,549,253,1030,122,20998,170,2798,3410,16933,290,
%T A174933 105449,362,161062,9320,10774,530,7984134,3151,17750,19936,617486,842,
%U A174933 24304630,962,1065509,36068,39598,42950,362923273,1370,55238,59498,102561574
%N A174933 a(n) = Sum_{d|n} A007955(d) * A000027(d) = Sum_{d|n} A007955(d) * (d), where A007955(m) = product of divisors of m.
%H A174933 Andrew Howroyd, <a href="/A174933/b174933.txt">Table of n, a(n) for n = 1..1000</a>
%e A174933 For n = 4, A007955(n) = b(n): a(4) = b(1)*1 + b(2)*2 + b(4)*4 = 1*1 + 2*2 + 8*4 = 37.
%o A174933 (PARI) a(n)={sumdiv(n, d, vecprod(divisors(d))*d)} \\ _Andrew Howroyd_, Jan 05 2020
%o A174933 (Magma) [&+[&*Divisors(d)*d:d in Divisors(n)]:n in [1..40]]; // _Marius A. Burtea_, Jan 05 2020
%o A174933 (Python)
%o A174933 from math import isqrt
%o A174933 from sympy import divisor_count, divisors
%o A174933 def A174933(n): return 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 A174933 Cf. A007955.
%K A174933 nonn
%O A174933 1,2
%A A174933 _Jaroslav Krizek_, Apr 02 2010
%E A174933 Terms a(31) and beyond from _Andrew Howroyd_, Jan 05 2020