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A341117
a(n) = Sum_{i+j>=m+1} d_i * d_j, where d_1 < ... < d_m are the divisors of n.
3
1, 8, 15, 44, 35, 129, 63, 208, 162, 305, 143, 712, 195, 553, 550, 912, 323, 1431, 399, 1665, 994, 1265, 575, 3356, 950, 1729, 1566, 3017, 899, 4901, 1023, 3840, 2266, 2873, 2254, 7845, 1443, 3553, 3094, 7744, 1763, 8862, 1935, 6897, 5901, 5129, 2303, 14672, 3234, 8475, 5134, 9425, 2915, 13986
OFFSET
1,2
COMMENTS
If p is prime, a(p^k) = (p^(2*k+2)-(2+k)*p^(k+1)+(k+1)*p^k)/(p - 1)^2.
If p < q are primes, a(p*q) = q*(p^2*q+2*p^2+2*p*q+4*p+q).
LINKS
EXAMPLE
The divisors of 6 are 1,2,3,6, so a(6) = 6*(1+2+3+6)+3*(2+3+6)+2*(3+6)+1*6 = 129.
MAPLE
f:= proc(n) local D, S, i;
D:= sort(convert(numtheory:-divisors(n), list), `>`);
S:= ListTools:-PartialSums(D);
add(D[i]*S[-i], i=1..nops(D))
end proc:
map(f, [$1..100]);
MATHEMATICA
Array[Sum[#1[[k]]*Sum[#1[[j]], {j, #2 - k + 1, #2}], {k, #2}] & @@ {Divisors[#], DivisorSigma[0, #]} &, 54] (* Michael De Vlieger, Feb 05 2021 *)
PROG
(PARI) a(n) = my(d=divisors(n)); sum(k=1, #d, d[k]*sum(i=#d-k+1, #d, d[i])); \\ Michel Marcus, Feb 05 2021
CROSSREFS
Sequence in context: A254541 A137658 A275277 * A255428 A367876 A216443
KEYWORD
nonn
AUTHOR
J. M. Bergot and Robert Israel, Feb 05 2021
STATUS
approved