_Paolo P. Lava & _ and _Giorgio Balzarotti (paoloplava(AT)gmail.com), _, Nov 26 2007

Terms a(7) onward from _Max Alekseyev (maxale(AT)gmail.com), _, Sep 24 2011

Paolo P. Lava & Giorgio Balzarotti (pplpaoloplava(AT)splgmail.atcom), Nov 26 2007

editing

approved

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

approved

editing

editing

approved

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

Is it the sequence finite?

easy,nonn,base

Terms a(7) onward from Max Alekseyev (maxale(AT)gmail.com), Sep 24 2011

approved

editing

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

1,1

Is it the sequence finite?

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

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);

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

easy,nonn,base,new

Paolo P. Lava & Giorgio Balzarotti (ppl(AT)spl.at), Nov 26 2007

approved