cp's OEIS Frontend

A341038 a(n) = Sum_{i+j<=m+1} d_i * d_j, where d_1 < ... < d_m are the divisors of n.

%I A341038 #14 Feb 04 2021 20:06:52
%S A341038 1,5,7,17,11,39,15,49,34,59,23,144,27,79,86,129,35,198,39,219,114,119,
%T A341038 47,436,86,139,142,287,59,523,63,321,170,179,190,760,75,199,198,676,
%U A341038 83,690,87,423,453,239,95,1184,162,474,254,491,107,846,278,896,282,299,119,2061,123,319,613,769
%N A341038 a(n) = Sum_{i+j<=m+1} d_i * d_j, where d_1 < ... < d_m are the divisors of n.
%C A341038 If p is prime, a(p^k) = k*p^(k+1)/(p-1) + ((p-2)*p^(k+1)+1)/(p-1)^2.
%C A341038 If p < q are primes, a(p*q) = 1 + 2*p + 2*q + p^2 + 4*p*q.
%H A341038 Robert Israel, <a href="/A341038/b341038.txt">Table of n, a(n) for n = 1..10000</a>
%e A341038 The divisors of 6 are 1,2,3,6, so a(6) = 1*(1+2+3+6)+2*(1+2+3)+3*(1+2)+6*1 = 39.
%p A341038 f:= proc(n) local D,S,i;
%p A341038   D:= sort(convert(numtheory:-divisors(n),list));
%p A341038   S:= ListTools:-PartialSums(D);
%p A341038   add(S[-i]*D[i],i=1..nops(D))
%p A341038 end proc:
%p A341038 map(f, [$1..100]);
%o A341038 (PARI) a(n) = my(d=divisors(n)); sum(k=1, #d, d[k]*sum(i=1, #d-k+1, d[i])); \\ _Michel Marcus_, Feb 04 2021
%Y A341038 Cf. A341039
%K A341038 nonn,look
%O A341038 1,2
%A A341038 _J. M. Bergot_ and _Robert Israel_, Feb 03 2021