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

Author

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

Keywords

• nonn
• look

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.

Examples

			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.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A341039

Programs

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]);

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