A345269 - OEIS

A345269

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

1, 2, 4, 6, 126, 11, 16808, 518, 59053, 1127, 2357947692, 1743, 1792160394038, 554633, 170859504, 268435974, 2862423051509815794, 1948628, 5480386857784802185940, 1280001131, 350277500559032, 1209627165485, 39471584120695485887249589624, 4586473679, 363797880709171295166015751

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

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

LINKS

Table of n, a(n) for n=1..25.

EXAMPLE

a(10) = Sum_{d|10} (10/d)^(phi(10/d) - 1) = 10^(4-1) + 5^(4-1) + 2^(1-1) + 1^(1-1) = 1000 + 125 + 1 + 1 = 1127.

MATHEMATICA

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

CROSSREFS