A373002 a(n) = Sum_{k=1..n} tau( (n/gcd(k,n))^n ).

1, 4, 9, 24, 25, 120, 49, 144, 135, 540, 121, 1728, 169, 1456, 2145, 800, 289, 5220, 361, 8840, 5985, 5544, 529, 21216, 1125, 9100, 1863, 25200, 841, 252000, 961, 4160, 23529, 20196, 31465, 94392, 1369, 28120, 38961, 113520, 1681, 991452, 1849, 101024, 118215

Offset

1,2

Links

Table of n, a(n) for n=1..45.

Formula

a(n) = n * A373003(n).

If p is prime, a(p) = p^2.

a(n) = Sum_{d|n} phi(d) * tau(d^n).

Prog

(PARI) a(n) = sumdiv(n, d, eulerphi(d)*numdiv(d^n));

Crossrefs

Cf. A062380, A062949, A372997, A372999.

Cf. A344223, A373003.

Sequence in context: A320913 A329879 A320059 * A270450 A270461 A046422

Adjacent sequences: A372999 A373000 A373001 * A373003 A373004 A373005

Keyword

nonn

Author

Seiichi Manyama, May 19 2024

Status

approved