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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. 2

%I #12 Sep 08 2022 08:45:51

%S 1,5,10,37,26,230,50,549,253,1030,122,20998,170,2798,3410,16933,290,

%T 105449,362,161062,9320,10774,530,7984134,3151,17750,19936,617486,842,

%U 24304630,962,1065509,36068,39598,42950,362923273,1370,55238,59498,102561574

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

%H Andrew Howroyd, <a href="/A174933/b174933.txt">Table of n, a(n) for n = 1..1000</a>

%e 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 (PARI) a(n)={sumdiv(n, d, vecprod(divisors(d))*d)} \\ _Andrew Howroyd_, Jan 05 2020

%o (Magma) [&+[&*Divisors(d)*d:d in Divisors(n)]:n in [1..40]]; // _Marius A. Burtea_, Jan 05 2020

%o (Python)

%o from math import isqrt

%o from sympy import divisor_count, divisors

%o 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 Cf. A007955.

%K nonn

%O 1,2

%A _Jaroslav Krizek_, Apr 02 2010

%E Terms a(31) and beyond from _Andrew Howroyd_, Jan 05 2020

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Last modified March 28 07:20 EDT 2024. Contains 371235 sequences. (Running on oeis4.)