A387662 a(n) is the least k>0 such that n divides 1^1 + 2^2 + ... + k^k.

1, 3, 4, 3, 2, 4, 9, 3, 4, 43, 16, 4, 8, 12, 18, 3, 8, 4, 9, 43, 15, 16, 33, 4, 49, 8, 7, 12, 11, 43, 22, 3, 51, 8, 21, 4, 144, 19, 87, 43, 8, 15, 14, 16, 53, 44, 19, 4, 40, 164, 17, 8, 14, 7, 68, 12, 18, 11, 150, 43, 38, 68, 15, 35, 99, 51, 151, 8, 33, 43, 41, 4, 18, 144

Offset

1,2

Links

Jason Yuen, Table of n, a(n) for n = 1..10000

Maple

a:= proc(n) local k; 0; for k
      do irem(%+k^k, n); if %=0 then return k fi od
    end:
seq(a(n), n=1..74);  # Alois P. Heinz, Oct 04 2025

Mathematica

a[n_]:=Module[{k=1}, While[!Divisible[Sum[i^i, {i, k}], n], k++]; k]; Array[a, 74] (* Stefano Spezia, Oct 04 2025 *)

Prog

(Python)
def a(n):
  s=k=0
  while 1:
    k+=1
    s=(s+pow(k, k, n))%n
    if s==0:
      return k
print([a(n) for n in range(1, 75)])
(PARI) a(n) = my(k=1, s=Mod(0, n)); while (lift(s+=Mod(k, n)^k), k++); k; \\ Michel Marcus, Oct 04 2025

Crossrefs

Cf. A000312, A001923.

Sequence in context: A164358 A275638 A281975 * A133617 A199286 A188722

Adjacent sequences: A387659 A387660 A387661 * A387663 A387664 A387665

Keyword

nonn,easy

Author

Alex Ratushnyak, Oct 04 2025

Status

approved