A045512 If decimal expansion of n is ab...d, a(n) = a^a + b^b + ... + d^d (ignoring any 0's).

0, 1, 4, 27, 256, 3125, 46656, 823543, 16777216, 387420489, 1, 2, 5, 28, 257, 3126, 46657, 823544, 16777217, 387420490, 4, 5, 8, 31, 260, 3129, 46660, 823547, 16777220, 387420493, 27, 28, 31, 54, 283, 3152, 46683, 823570, 16777243, 387420516, 256, 257, 260

Offset: 0

Author

N. J. A. Sloane, Jeff Burch

Keywords

• nonn
• base

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A045503.

See A046253 for fixed points.

Programs

Maple

a:= n-> add(`if`(i=0, 0, i^i), i=convert(n,base,10)):
seq(a(n), n=0..42);  # Alois P. Heinz, Apr 29 2022

Mathematica

p[n_]:=Module[{idn=Select[IntegerDigits[n],#>0&]},Total[idn^idn]]; Array[p, 40,0] (* Harvey P. Dale, Dec 13 2012 *)

PARI

apply( {A045512(n)=vecsum([d^d|d<-digits(n),d])}, [0..44]) \\ M. F. Hasler, Oct 01 2024

Extensions

Checked by Neven Juric (neven.juric(AT)apis-it.hr), Feb 04 2008