A343513 a(n) = Sum_{k=1..n} (k/gcd(n, k))^3.

1, 2, 10, 30, 101, 137, 442, 526, 1063, 1202, 3026, 1965, 6085, 4853, 7310, 8654, 18497, 10100, 29242, 17630, 29557, 30857, 64010, 30397, 77601, 60842, 89272, 71913, 164837, 60737, 216226, 139470, 188165, 180338, 265142, 152544, 443557, 282665, 371134, 275726, 672401, 251066, 815410, 461645

Offset

1,2

Comments

a(n) = 1+n^2*(n-1)^2/4 if n is prime. - Robert Israel, Apr 19 2021

Links

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

Formula

a(n) = Sum_{d|n} A053819(d).

Maple

f:= proc(n) local k;
  add((k/igcd(n, k))^3, k=1..n)
end proc:
map(f, [$1..100]); # Robert Israel, Apr 19 2021

Mathematica

Table[Sum[(k/GCD[n, k])^3, {k, 1, n}], {n, 1, 44}]

Prog

(PARI) a(n) = sum(k=1, n, (k/gcd(n, k))^3); \\ Michel Marcus, Apr 17 2021

Crossrefs

Cf. A053819, A057661, A332654, A343497, A343514.

Sequence in context: A196317 A318579 A064932 * A285956 A219667 A192381

Adjacent sequences: A343510 A343511 A343512 * A343514 A343515 A343516

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 17 2021

Status

approved