login
A343513
a(n) = Sum_{k=1..n} (k/gcd(n, k))^3.
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
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
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Apr 17 2021
STATUS
approved