A135202 Numbers n that raised to the powers from 1 to k (with k>=1) are multiples of the sum of their digits (n raised to k+1 must not be a multiple). Case k=17.

3900, 39000, 390000, 3900000, 12432420, 16528050, 19211220, 28845180, 29549520, 29895180, 34310100, 34899480, 36659700, 39000000, 39159120, 48452040, 51092580, 53295000, 66156090, 83393310, 95416230, 100960860, 109052580, 117865440, 124324200

Offset

1,1

Links

Table of n, a(n) for n=1..25.

Formula

Positive integers n such that A195860(n)=18.

Example

3900^1=3900 is multiple of Sum_digits(3900)=12
3900^2=15210000 is multiple of Sum_digits(3900^2)=9
...
3900^17 is a multiple of Sum_digits(3900^17)=108
while
3900^18 is not multiple of Sum_digits(3900^18)=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(50000, 17);

Crossrefs

Cf. A135186, A135187, A135188, A135189, A135190, A135191, A135192, A135193, A135194, A135195, A135196, A135197, A135198, A135199, A135200, A135201.

Sequence in context: A242863 A247691 A242873 * A204147 A252138 A115468

Adjacent sequences: A135199 A135200 A135201 * A135203 A135204 A135205

Keyword

nonn,base

Author

Paolo P. Lava and Giorgio Balzarotti, Nov 26 2007

Extensions

Terms a(4) onward from Max Alekseyev, Sep 24 2011

Status

approved