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%I #10 Sep 08 2022 08:46:21
%S 1,5,7,29,11,155,15,285,88,415,23,10547,27,803,917,5405,35,35228,39,
%T 48439,1785,1963,47,2665011,386,2735,3004,132539,59,6481465,63,202013,
%U 4385,4663,4925,90744884,75,5819,6117,20528695,83,24896285,87,513091,547748,8515
%N a(n) = Sum_{d|n} (tau(d)*pod(d)) where tau(k) = the number of divisors of k (A000005) and pod(k) = the product of the divisors of k (A007955).
%C n divides a(n) for n = 1, 21, 333592, ...
%F a(p) = 2*(p+1) for p = primes (A000040).
%e a(6) = tau(1)*pod(1) + tau(2)*pod(2) + tau(3)*pod(3) + tau(6)*pod(6) = (1*1) + (2*2) + (2*3) + (4*36) = 155.
%o (Magma) [&+[# [c: c in Divisors(d)] * &*[c: c in Divisors(d)]: d in Divisors(n)]: n in [1..100]]
%o (PARI) a(n) = sumdiv(n, d, my(dd=divisors(d)); #dd*vecprod(dd)); \\ _Michel Marcus_, Apr 25 2019
%Y Cf. A000005, A007955, A307101.
%K nonn
%O 1,2
%A _Jaroslav Krizek_, Apr 25 2019
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