A135201 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=16.

210, 2100, 2310, 14490, 21000, 23100, 100020, 144900, 210000, 231000, 397320, 424830, 1000200, 1113420, 1449000, 2100000, 2310000, 3619770, 3973200, 4248300, 5349960, 5397000, 7773150, 8851920, 10002000, 11134200, 12035100, 14490000, 15496740

Offset

1,1

Links

Table of n, a(n) for n=1..29.

Formula

Positive integers n such that A195860(n)=17.

Example

210^1=210 is multiple of Sum_digits(210)=3
210^2=44100 is multiple of Sum_digits(44100)=9
...
210^16=14305686902419853283210000000000000000 is a multiple of Sum_digits(210^16)=90
while
210^17=3004194249508169189474100000000000000000 is not multiple of Sum_digits(210^17)=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(45000, 16);

Crossrefs

Cf. A135186, A135187, A135188, A135189, A135190, A135191, A135192, A135193, A135194, A135195, A135196, A135197, A135198, A135199, A135200, A135202.

Sequence in context: A104902 A371111 A371053 * A187663 A064260 A027806

Adjacent sequences: A135198 A135199 A135200 * A135202 A135203 A135204

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