A135198 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=13.

780, 1890, 4620, 5040, 7800, 12360, 18900, 20610, 22950, 46200, 50400, 61950, 74550, 78000, 90090, 107730, 123600, 128520, 144060, 189000, 206100, 212940, 220290, 229500, 247170, 273210, 301410, 323190, 416430, 427980, 433650, 462000, 504000

Offset

1,1

Links

Table of n, a(n) for n=1..33.

Formula

Positive integers n such that A195860(n)=14.

Example

780^1=780 is multiple of Sum_digits(780)=15
780^2=608400 is multiple of Sum_digits(608400)=18
etc. till
780^13=39557590922648009090580480000000000000 is a multiple of Sum_digits(39557590922648009090580480000000000000)=117
while
780^14=30854920919665447090652774400000000000000 is not multiple of Sum_digits(30854920919665447090652774400000000000000)=126

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(25000, 13);

Crossrefs

Cf. A135186, A135187, A135188, A135189, A135190, A135191, A135192, A135193, A135194, A135195, A135196, A135197, A135199, A135200, A135201, A135202.

Sequence in context: A341190 A147547 A259924 * A292063 A250952 A139400

Adjacent sequences: A135195 A135196 A135197 * A135199 A135200 A135201

Keyword

nonn,base

Author

Paolo P. Lava and Giorgio Balzarotti, Nov 23 2007

Extensions

Terms a(10) onward from Max Alekseyev, Sep 24 2011

Status

approved