A135200 - OEIS

A135200

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=15.

3780, 10050, 15750, 32760, 37800, 39060, 100500, 153720, 157500, 203280, 267960, 327600, 378000, 387720, 390600, 460350, 630630, 1005000, 1032570, 1537200, 1575000, 2032800, 2679600, 3276000, 3575880, 3780000, 3877200, 3906000, 4603500, 4696230

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OFFSET

1,1

LINKS

Table of n, a(n) for n=1..30.

FORMULA

Positive integers n such that A195860(n)=16.

EXAMPLE

3780^1=3780 is multiple of Sum_digits(3780)=18

3780^2=14288400 is multiple of Sum_digits(14288400)=27

...

3780^15=459596801440358960392275509579197612032000000000000000 is a multiple of Sum_digits(459596801440358960392275509579197612032000000000000000)=180

while

3780^16=1737275909444556870282801426209366973480960000000000000000 is not multiple of Sum_digits(1737275909444556870282801426209366973480960000000000000000)=198

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(40000, 15);

CROSSREFS

Cf. A135186, A135187, A135188, A135189, A135190, A135191, A135192, A135193, A135194, A135195, A135196, A135197, A135198, A135199, A135201, A135202.

Sequence in context: A080953 A178193 A243777 * A348148 A186953 A107539

Adjacent sequences: A135197 A135198 A135199 * A135201 A135202 A135203

KEYWORD

nonn,base

AUTHOR

Paolo P. Lava and Giorgio Balzarotti, Nov 26 2007

EXTENSIONS

Terms a(7) onward from Max Alekseyev, Sep 24 2011

STATUS

approved