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A341038 a(n) = Sum_{i+j<=m+1} d_i * d_j, where d_1 < ... < d_m are the divisors of n. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 25 20:01 EDT 2021. Contains 347659 sequences. (Running on oeis4.)