A135199 Numbers n that raised to the powers from 1 to k (with k>=1) are multiples of the sum of their digits (and n raised to k+1 must not be such a multiple). Case k=14.

60, 150, 600, 1500, 3390, 4320, 6000, 9240, 15000, 33900, 43200, 51810, 60000, 92400, 150000, 288750, 339000, 432000, 518100, 600000, 612150, 686070, 794640, 924000, 1043460, 1122450, 1225350, 1305150, 1483020, 1500000, 1711710, 2125620, 2174970

Offset

1,1

Links

Table of n, a(n) for n=1..33.

Formula

Positive integers n such that A195860(n)=15.

Example

60^1=60 is multiple of Sum_digits(60)=6
60^2=3600 is multiple of Sum_digits(3600)=9
...
60^14=7836416409600000000000000 is a multiple of Sum_digits(7836416409600000000000000)=54
while
60^15=470184984576000000000000000 is not multiple of Sum_digits(470184984576000000000000000)=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(30000, 14);

Mathematica

msdQ[n_]:=Module[{b=Boole[Divisible[#, Total[IntegerDigits[#]]]&/@(n^Range[ 15])]}, Total[b]==14&&Last[b]==0]; Select[Range[22*10^5], msdQ] (* Harvey P. Dale, Apr 07 2019 *)

Crossrefs

Cf. A135186, A135187, A135188, A135189, A135190, A135191, A135192, A135193, A135194, A135195, A135196, A135197, A135198, A135200, A135201, A135202.

Sequence in context: A039497 A218243 A218392 * A112065 A252018 A044392

Adjacent sequences: A135196 A135197 A135198 * A135200 A135201 A135202

Keyword

nonn,base

Author

Paolo P. Lava and Giorgio Balzarotti, Nov 26 2007

Extensions

Terms a(10) onward from Max Alekseyev, Sep 24 2011

Definition clarified by Harvey P. Dale, Apr 07 2019

Status

approved