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 A046017 Least k > 1 with k = sum of digits of k^n, or 0 if no such k exists. 9

%I

%S 2,9,8,7,28,18,18,46,54,82,98,108,20,91,107,133,80,172,80,90,90,90,

%T 234,252,140,306,305,90,305,396,170,388,170,387,378,388,414,468,449,

%U 250,432,280,461,280,360,360,350,370,270,685,360,625,648,370,677,684,370,667,370,694,440,855,827,430,818

%N Least k > 1 with k = sum of digits of k^n, or 0 if no such k exists.

%C First non-occurrence happens with exponent 105. There is no x such that sum-of-digits{x^105}=x (x>1). - _Patrick De Geest_, Aug 15 1998

%D G. Balzarotti and P. P. Lava, Le sequenze di numeri interi, Hoepli, 2008, p. 208-210.

%D Joe Roberts, "Lure of the Integers", The Mathematical Association of America, 1992, p. 172.

%H T. D. Noe, <a href="/A046017/b046017.txt">Table of n, a(n) for n=1..1000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ClassNumber.html">Class Number.</a>

%e a(3) = 8 since 8^3 = 512 and 5+1+2 = 8; a(5) = 28 because 28 is least number > 1 with 28^5 = 17210368, 1+7+2+1+0+3+6+8 = 28. 53^7 = 1174711139837 -> 1+1+7+4+7+1+1+1+3+9+8+3+7 = 53.

%e a(10) = 82 because 82^10 = 13744803133596058624 and 1 + 3 + 7 + 4 + 4 + 8 + 0 + 3 + 1 + 3 + 3 + 5 + 9 + 6 + 0 + 5 + 8 + 6 + 2 + 4 = 82.

%e a(13) = 20: 20^13=81920000000000000, 8+1+9+2=20.

%e a(17) = 80: 80^17=225179981368524800000000000000000, 2+2+5+1+7+9+9+8+1+3+6+8+5+2+4+8 = 80.

%t a[n_] := For[k = 2, k <= 20*n, k++, Which[k == Total[IntegerDigits[k^n]], Return[k], k == 20*n, Return[0]]]; Table[a[n] , {n, 1, 105}] (* _Jean-François Alcover_, May 23 2012 *)

%Y Cf. A046459, A046000, A046471, A061211.

%Y Cf. A133509 (n for which a(n)=0), A152147 (table of k for each n).

%K base,nonn,nice

%O 1,1

%A _David W. Wilson_

%E More terms from Asher Natan Auel (auela(AT)reed.edu), Jun 01 2000

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Last modified June 13 10:32 EDT 2021. Contains 344987 sequences. (Running on oeis4.)