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

1,2

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

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

Prog

(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

Crossrefs

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

Sequence in context: A239589 A203614 A252069 * A013590 A216918 A278569

Adjacent sequences: A133506 A133507 A133508 * A133510 A133511 A133512

Keyword

nonn,base

Author

Farideh Firoozbakht, Dec 04 2007

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

Status

approved