OFFSET
1,2
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
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Jun 07 2021
STATUS
approved