A135197 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=12.

90, 120, 900, 1200, 3480, 4650, 5700, 7140, 9000, 12000, 13140, 13260, 21180, 21660, 25320, 28560, 30720, 33660, 34800, 41580, 46500, 57000, 60690, 71400, 81420, 88110, 90000, 108450, 120000, 131400, 132600, 145710, 211800, 216180, 216600, 224490

Offset

1,1

Links

Table of n, a(n) for n=1..36.

Formula

Positive integers n such that A195860(n)=13.

Example

90^1=90 is multiple of Sum_digits(90)=9
90^2=8100 is multiple of Sum_digits(8100)=9
etc. till
90^12=282429536481000000000000 is multiple of Sum_digits(282429536481000000000000)=54
while
90^13=25418658283290000000000000 is not multiple of Sum_digits(25418658283290000000000000)=63

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, 12);

Crossrefs

Cf. A135186, A135187, A135188, A135189, A135190, A135191, A135192, A135193, A135194, A135195, A135196, A135198, A135199, A135200, A135201, A135202.

Sequence in context: A044004 A078493 A176683 * A025371 A025362 A114826

Adjacent sequences: A135194 A135195 A135196 * A135198 A135199 A135200

Keyword

nonn,base

Author

Paolo P. Lava and Giorgio Balzarotti, Nov 23 2007

Extensions

Terms a(15) onward from Max Alekseyev, Sep 24 2011

Status

approved