A220365 a(n) is conjectured to be the largest power k for which k divides the sum of digits of n^k.

1, 70, 486, 35, 10, 90, 805, 5218, 243, 1, 35, 1494, 469004, 1045, 288, 116, 7, 195, 29, 70, 16710, 23, 2, 1017, 28, 58, 162, 166, 209, 486, 205, 106, 1206, 2053, 37120

Offset: 1

Author

Robert G. Wilson v, Dec 12 2012

Keywords

• base
• nonn

Comments

a(36) >= 423378.

Please consult the argument in A067863 for the reason that it is believed that all individual such sequences (all k's which divide b^k) terminate.

Examples

			a(2) = 70 since the sum of digits of 2^70 is divisible by 70 and it is believed that there does not exist any larger exponent which satisfies this criterion.
		

Crossrefs

Numbers n such that n divides the sum of digits of k^n: A175169 (k=2), A067862 (k=3), A067864 (k=6), A067863 (k=7), A062933 (k=8), A062927 (k=9), A175525 (k=13), A175589 (k=21), A220364 (k=36), A175552 (k=167).

Programs

Mathematica

For any individual base, b, fQ[n_] := Mod[Plus @@ IntegerDigits[b^n], n] == 0; k = 1; lst = {}; While[k < 100001, If[ fQ@ k, AppendTo[lst, k]; Print[k]]; k++]; lst

Formula

If a(n) = k, then a(10*n) = k.

Extensions

Definition and example corrected by Giovanni Resta, Dec 14 2012