OFFSET
1,2
COMMENTS
If p is prime, a(p^k) = k*p^(k+1)/(p-1) + ((p-2)*p^(k+1)+1)/(p-1)^2.
If p < q are primes, a(p*q) = 1 + 2*p + 2*q + p^2 + 4*p*q.
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
EXAMPLE
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.
MAPLE
f:= proc(n) local D, S, i;
D:= sort(convert(numtheory:-divisors(n), list));
S:= ListTools:-PartialSums(D);
add(S[-i]*D[i], i=1..nops(D))
end proc:
map(f, [$1..100]);
PROG
(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
CROSSREFS
KEYWORD
nonn,look
AUTHOR
J. M. Bergot and Robert Israel, Feb 03 2021
STATUS
approved