A342420 a(n) = Sum_{k=1..n} (n/gcd(k,n))^(n/gcd(k,n)).

1, 5, 55, 517, 12501, 93371, 4941259, 67109381, 2324522989, 40000012505, 2853116706111, 35664401886907, 3634501279107037, 66672040958289359, 3503151123046887555, 147573952589743522309, 13235844190181388226833, 236078448451781550068849, 35611553801885644604231623

Offset

1,2

Links

Table of n, a(n) for n=1..19.

Formula

a(n) = Sum_{d|n} phi(d^(d+1)) = Sum_{d|n} phi(d) * d^d.

G.f.: Sum_{k>=1} phi(k^(k+1))*x^k/(1 - x^k).

Mathematica

a[n_] := Sum[(n/GCD[k, n])^(n/GCD[k, n]), {k, 1, n}]; Array[a, 20] (* Amiram Eldar, Mar 11 2021 *)

Prog

(PARI) a(n) = sum(k=1, n, (n/gcd(k, n))^(n/gcd(k, n)));
(PARI) a(n) = sumdiv(n, d, eulerphi(d^(d+1)));
(PARI) a(n) = sumdiv(n, d, eulerphi(d)*d^d);
(PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, eulerphi(k^(k+1))*x^k/(1-x^k)))

Crossrefs

Cf. A000010, A226459, A342411.

Sequence in context: A247775 A045640 A043040 * A226561 A062183 A002279

Adjacent sequences: A342417 A342418 A342419 * A342421 A342422 A342423

Keyword

nonn

Author

Seiichi Manyama, Mar 11 2021

Status

approved