A342411 a(n) = Sum_{k=1..n} (n/gcd(k,n))^(n/gcd(k,n) - 2).

1, 2, 7, 34, 501, 2600, 100843, 1048610, 28697821, 400000502, 23579476911, 247669459528, 21505924728445, 340163474352620, 15569560546875507, 576460752304472098, 45798768824157052689, 728637186579594211070, 98646963440126439346903

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-2).

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] - 2), {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)-2));
(PARI) a(n) = sumdiv(n, d, eulerphi(d^(d-1)));
(PARI) a(n) = sumdiv(n, d, eulerphi(d)*d^(d-2));
(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, A342412.

Sequence in context: A222868 A222777 A222891 * A231580 A182408 A057298

Adjacent sequences: A342408 A342409 A342410 * A342412 A342413 A342414

Keyword

nonn

Author

Seiichi Manyama, Mar 11 2021

Status

approved