A345092 a(n) = Sum_{d|n} n^(phi(n/d) - 1).

1, 2, 4, 6, 126, 14, 16808, 522, 59059, 2002, 2357947692, 1766, 1792160394038, 1075650, 170862766, 268439570, 2862423051509815794, 3779174, 5480386857784802185940, 1280016022, 350277504626344, 2414538435586, 39471584120695485887249589624, 4586499146

Offset

1,2

Links

Table of n, a(n) for n=1..24.

Formula

a(p) = Sum_{d|p} p^(phi(p/d) - 1) = p^((p-1)-1) + p^0 = p^(p-2) + 1, for prime p.

Example

a(6) = Sum_{d|6} 6^(phi(6/d) - 1) = 6^(phi(6) - 1) + 6^(phi(3) - 1) + 6^(phi(2) - 1) + 6^(phi(1) - 1) = 6^1 + 6^1 + 6^0 + 6^0 = 14.

Mathematica

Table[Sum[n^(EulerPhi[n/k^(1 - Ceiling[n/k] + Floor[n/k])] - 1) (1 - Ceiling[n/k] + Floor[n/k]), {k, n}], {n, 30}]

Prog

(PARI) a(n) = sumdiv(n, d, n^(eulerphi(n/d)-1)); \\ Michel Marcus, Jun 07 2021

Crossrefs

Cf. A000010 (phi).

Sequence in context: A259050 A066719 A345269 * A033319 A185151 A218087

Adjacent sequences: A345089 A345090 A345091 * A345093 A345094 A345095

Keyword

nonn

Author

Wesley Ivan Hurt, Jun 07 2021

Status

approved