A133509 Numbers k such that m=1 is the only number for which the sum of digits of m^k equals m.

0, 105, 164, 186, 194, 206, 216, 231, 254, 282, 285, 302, 314, 324, 374, 386, 402, 416, 456, 468, 491, 504, 521, 552, 588, 606, 610, 615, 629, 651, 656, 657, 696, 759, 794, 830, 842, 854, 870, 903, 906, 954, 956, 981, 998, 1029, 1064, 1079, 1082, 1109, 1112, 1131

Offset: 1

Author

Farideh Firoozbakht, Dec 04 2007

Keywords

• nonn
• base

Links

• Carole Dubois, Table of n, a(n) for n = 1..226 (terms 1..100 from Michael S. Branicky)
• Carole Dubois, Pin plot of A133509

Crossrefs

Cf. A046000, A046017, A046019, A046471, A061211, A152147.

Programs

Python

def ok(n):
    d, lim = 1, 1
    while lim < n*9*d: d, lim = d+1, lim*10
    return not any(sum(map(int, str(k**n))) == k for k in range(2, lim+1))
for k in range(195):
    if ok(k): print(k, end=", ") # Michael S. Branicky, Jul 06 2022

Formula

If t is a term, A046000(t)=1, A046017(t)=0, A046019(t)=1, A046471(t)=0 and A061211(t)=1. - Mohammed Yaseen, Jun 29 2022

Extensions

Description improved by T. D. Noe, Nov 26 2008

Extension by T. D. Noe, Nov 26 2008

Edited by Charles R Greathouse IV, Aug 02 2010

a(1) = 0 and a(46) and beyond from Michael S. Branicky, Jul 06 2022