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

1, 5, 7, 17, 11, 39, 15, 49, 34, 59, 23, 144, 27, 79, 86, 129, 35, 198, 39, 219, 114, 119, 47, 436, 86, 139, 142, 287, 59, 523, 63, 321, 170, 179, 190, 760, 75, 199, 198, 676, 83, 690, 87, 423, 453, 239, 95, 1184, 162, 474, 254, 491, 107, 846, 278, 896, 282, 299, 119, 2061, 123, 319, 613, 769

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

Cf. A341039

Sequence in context: A318491 A060640 A064944 * A070372 A082818 A224070

Adjacent sequences: A341035 A341036 A341037 * A341039 A341040 A341041

Keyword

nonn,look

Author

J. M. Bergot and Robert Israel, Feb 03 2021

Status

approved