A345268 a(n) = Sum_{d|n} d^(phi(n/d) - 1).

1, 2, 2, 3, 2, 5, 2, 5, 5, 11, 2, 12, 2, 35, 34, 15, 2, 44, 2, 80, 252, 515, 2, 56, 127, 2051, 254, 1066, 2, 389, 2, 203, 19696, 32771, 3470, 1113, 2, 131075, 177162, 842, 2, 10091, 2, 262670, 6058, 2097155, 2, 2634, 16809, 525416, 14348926, 4196368, 2, 139121, 1954458, 36200

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..56.

Example

a(14) = Sum_{d|14} d^(phi(14/d) - 1) = 1^(6-1) + 2^(6-1) + 7^(1-1) + 14^(1-1) = 1 + 32 + 1 + 1 = 35.

Mathematica

Table[Sum[k^(EulerPhi[n/k^(1 - Ceiling[n/k] + Floor[n/k])] - 1) (1 - Ceiling[n/k] + Floor[n/k]), {k, n}], {n, 60}]

Crossrefs

Cf. A345092.

Sequence in context: A062830 A322366 A363724 * A164941 A328673 A115119

Adjacent sequences: A345265 A345266 A345267 * A345269 A345270 A345271

Keyword

nonn

Author

Wesley Ivan Hurt, Jun 12 2021

Status

approved