cp's OEIS Frontend

A325029 a(n) = Sum_{d|n} (sigma(d)*pod(d)) where sigma(k) = the sum of the divisors of k (A000203) and pod(k) = the product of the divisors of k (A007955).

%I A325029 #8 Sep 08 2022 08:46:24
%S A325029 1,7,13,63,31,451,57,1023,364,1837,133,48891,183,4767,5443,32767,307,
%T A325029 228250,381,337893,14181,17563,553,19956411,3906,28581,29524,1234135,
%U A325029 871,58327681,993,2097151,52417,62737,58887,917347026,1407,87027,85371,230738853,1723
%N A325029 a(n) = Sum_{d|n} (sigma(d)*pod(d)) where sigma(k) = the sum of the divisors of k (A000203) and pod(k) = the product of the divisors of k (A007955).
%C A325029 n divides a(n) for n = 1, 39, 793, 2800, 5289, 6601, 15747, 41041, ...
%F A325029 a(p) = p^2 + p + 1 for p = primes (A000040).
%e A325029 a(6) = sigma(1)*pod(1) + sigma(2)*pod(2) + sigma(3)*pod(3) + sigma(6)*pod(6) = (1*1) + (3*2) + (4*3) + (12*36) = 451.
%o A325029 (Magma) [&+[&+ [c: c in Divisors(d)] * &*[c: c in Divisors(d)]: d in Divisors(n)]: n in [1..100]]
%o A325029 (PARI) a(n) = sumdiv(n, d, my(dd=divisors(d)); vecsum(dd)*vecprod(dd)); \\ _Michel Marcus_, Apr 25 2019
%Y A325029 Cf. A000203, A007955, A325030.
%K A325029 nonn
%O A325029 1,2
%A A325029 _Jaroslav Krizek_, Apr 25 2019