login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A332620 a(n) = Sum_{k=1..n} n^(n/gcd(n, k)). 5
1, 6, 57, 532, 12505, 93786, 4941265, 67117128, 2324524401, 40000400110, 2853116706121, 35664407810076, 3634501279107049, 66672041585829330, 3503151123049919265, 147573952606856413456, 13235844190181388226849, 236078448452969449231206, 35611553801885644604231641 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..385

FORMULA

a(n) = [x^n] Sum_{k>=1} Sum_{j>=1} phi(j) * n^j * x^(k*j).

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

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

a(n) = n * A332621(n).

MATHEMATICA

Table[Sum[n^(n/GCD[n, k]), {k, 1, n}], {n, 1, 19}]

Table[Sum[EulerPhi[d] n^d, {d, Divisors[n]}], {n, 1, 19}]

Table[SeriesCoefficient[Sum[Sum[EulerPhi[j] n^j x^(k j), {j, 1, n}], {k, 1, n}], {x, 0, n}], {n, 1, 19}]

PROG

(MAGMA) [&+[n^(n div Gcd(n, k)):k in [1..n]]:n in [1..20]]; // Marius A. Burtea, Feb 17 2020

(PARI) a(n) = sum(k=1, n, n^(n/gcd(n, k))); \\ Michel Marcus, Mar 10 2021

CROSSREFS

Cf. A000010, A056665, A066108, A226561, A228640, A321349, A332621.

Sequence in context: A144070 A095900 A161434 * A246235 A213105 A138414

Adjacent sequences:  A332617 A332618 A332619 * A332621 A332622 A332623

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Feb 17 2020

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 20 12:58 EDT 2021. Contains 343135 sequences. (Running on oeis4.)