A108860 Numbers k that divide the sum of the digits of (2k)^k.

1, 3, 9, 12, 16, 18, 22, 27, 29, 33, 48, 54, 80, 127, 133, 149, 171, 335, 888, 1038, 1137, 1435, 1465, 1647, 13921, 14256, 22467, 22872, 23514, 23709, 39564, 108708, 108777, 109308, 230115, 837117

Offset

1,2

Comments

The quotients are 2, 3, 7, 6, 7, 7, 7, 8, 8, 9, 9, 9, 5, 11, 11, 11, 11, 8, 15, 15, 15, 11, 11, 16, 20, 20, 21, 21, 21, 21, 22, 24, 24, 24, 21, 28.

Links

Table of n, a(n) for n=1..36.

Example

888 is a term because the sum of the digits of (2*888)^888, 13320, is divisible by 888.

Mathematica

Do[If[Mod[Plus @@ IntegerDigits[(2*n)^n], n] == 0, Print[n]], {n, 1, 10000}]

Prog

(Python)
A108860_list = [n for n in range(1, 1000) if not sum(int(d) for d in str((2*n)**n)) % n] # Chai Wah Wu, Mar 15 2018

Crossrefs

Cf. A062971.

Sequence in context: A244147 A103531 A333441 * A006499 A310320 A274676

Adjacent sequences: A108857 A108858 A108859 * A108861 A108862 A108863

Keyword

nonn,base,hard,more

Author

Ryan Propper, Jul 11 2005

Extensions

a(25)-a(26) from Harvey P. Dale, Nov 24 2010

a(27)-a(35) from Lars Blomberg, Jul 02 2011

a(36) from Kevin P. Thompson, Apr 15 2022

Status

approved