A135188 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=3.

2, 20, 72, 80, 84, 108, 112, 156, 198, 200, 216, 324, 351, 378, 504, 522, 558, 612, 684, 738, 800, 902, 918, 936, 972, 1008, 1011, 1040, 1098, 1101, 1212, 1242, 1368, 1386, 1416, 1452, 1602, 1611, 1656, 1674, 1818, 1836, 1908, 1998, 2000, 2088, 2178

Offset

1,1

Links

Table of n, a(n) for n=1..47.

Formula

Positive integers n such that A195860(n) = 4.

Example

20^1=20, sum_digits(20)=2, and 20 is a multiple of 2;
20^2=400, sum_digits(400)=4, and 400 is a multiple of 4;
20^3=8000, sum_digits(8000)=8, and 8000 is a multiple of 8;
20^4=160000, sum_digits(160000)=7, and 160000 is not a multiple of 7.

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, 3);

Crossrefs

Cf. A135186, A135187, A135189, A135190, A135191, A135192, A135193, A135194, A135195, A135196, A135197, A135198, A135199, A135200, A135201, A135202.

Sequence in context: A287485 A003283 A259110 * A161007 A331760 A098077

Adjacent sequences: A135185 A135186 A135187 * A135189 A135190 A135191

Keyword

nonn,base

Author

Paolo P. Lava & Giorgio Balzarotti, Nov 22 2007

Extensions

More terms from Max Alekseyev, Sep 24 2011

Status

approved