A135196 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=11.

420, 990, 1680, 4200, 9900, 12060, 12870, 13230, 16800, 17010, 25500, 33570, 37380, 42000, 53250, 65310, 75810, 80010, 99000, 102750, 115710, 117810, 120600, 128700, 132300, 143640, 155430, 168000, 170100, 187110, 191610, 211860, 213180, 219450

Offset

1,1

Links

Table of n, a(n) for n=1..34.

Formula

Positive integers n such that A195860(n)=12.

Example

420^1=420 is multiple of Sum_digits(420)=6
420^2=176400 is multiple of Sum_digits(176400)=18
etc. till
420^11=71736832111046860800000000000 is multiple of Sum_digits(71736832111046860800000000000)=72
while
420^12=30129469486639681536000000000000 is not multiple of Sum_digits(30129469486639681536000000000000)=99

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(15000, 11);

Crossrefs

Cf. A135186, A135187, A135188, A135189, A135190, A135191, A135192, A135193, A135194, A135195, A135197, A135198, A135199, A135200, A135201, A135202.

Sequence in context: A191934 A147775 A169825 * A259025 A281210 A235233

Adjacent sequences: A135193 A135194 A135195 * A135197 A135198 A135199

Keyword

nonn,base

Author

Paolo P. Lava and Giorgio Balzarotti, Nov 23 2007

Extensions

Terms a(9) onward from Max Alekseyev, Sep 24 2011

Status

approved