A135187 - OEIS

A135187

Numbers n that raised to the powers from 1 to k (with k>=1) are multiple of the sum of their digits (n raised to k+1 must not be a multiple). Case k=2.

9, 21, 45, 63, 117, 132, 140, 144, 190, 201, 204, 207, 220, 243, 264, 288, 315, 333, 402, 414, 441, 460, 476, 506, 513, 531, 550, 552, 594, 603, 621, 648, 666, 702, 770, 774, 828, 846, 864, 880, 954, 999, 1012, 1017, 1032, 1044, 1053, 1056, 1062

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OFFSET

1,1

LINKS

Table of n, a(n) for n=1..49.

FORMULA

Positive integers n such that A195860(n)=3.

EXAMPLE

9^1 = 9; 9^2 = 81, sum_digits(81) = 9, and 81 is a multiple of 9; 9^3 = 729, sum_digits(729) = 18, and 729 is not a multiple of 18.

MAPLE

readlib(log10); P:=proc(n, m) local a, i, k, w, x, ok; for i from 1 by 1 to n do a:=simplify(log10(i)); if not (trunc(a)=a) then ok:=1; x:=1; while ok=1 do w:=0; k:=i^x; while k>0 do w:=w+k-(trunc(k/10)*10); k:=trunc(k/10); od; if trunc(i^x/w)=i^x/w then x:=x+1; else if x-1=m then print(i); fi; ok:=0; fi; od; fi; od; end: P(2000, 2);

CROSSREFS

Cf. A135186 - A135202.

Sequence in context: A231570 A020190 A225507 * A246318 A277715 A173391

Adjacent sequences: A135184 A135185 A135186 * A135188 A135189 A135190

KEYWORD

nonn,base

AUTHOR

Paolo P. Lava & Giorgio Balzarotti, Nov 22 2007

EXTENSIONS

More terms from Max Alekseyev, Sep 24 2011

STATUS

approved