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A133509
Numbers k such that m=1 is the only number for which the sum of digits of m^k equals m.
7
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
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