A344484 a(n) = Sum_{d|n} d^phi(n/d).

1, 3, 4, 7, 6, 14, 8, 17, 19, 32, 12, 48, 14, 86, 122, 57, 18, 137, 20, 328, 800, 1058, 24, 250, 651, 4136, 838, 4252, 30, 1804, 32, 625, 59204, 65588, 18062, 4557, 38, 262202, 531650, 5394, 42, 51790, 44, 1049788, 29018, 4194374, 48, 8906, 117699, 1059277, 43047062

Offset

1,2

Comments

If p is prime, a(p) = Sum_{d|p} d^phi(p/d) = 1^(p-1) + p^1 = p + 1.

Links

Table of n, a(n) for n=1..51.

Example

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

Mathematica

Table[Sum[k^EulerPhi[n/k^(1 - Ceiling[n/k] + Floor[n/k])] (1 - Ceiling[n/k] + Floor[n/k]), {k, n}], {n, 80}]

Prog

(PARI) a(n) = sumdiv(n, d, d^eulerphi(n/d)); \\ Michel Marcus, May 21 2021

Crossrefs

Cf. A000010, A018804, A174476.

Sequence in context: A215509 A053480 A258052 * A241448 A323243 A346193

Adjacent sequences: A344481 A344482 A344483 * A344485 A344486 A344487

Keyword

nonn

Author

Wesley Ivan Hurt, May 20 2021

Status

approved