A135193 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=8.

180, 252, 720, 1350, 1800, 2040, 2520, 3324, 3870, 5520, 6552, 6750, 7200, 7812, 8220, 8280, 8964, 9450, 10080, 10098, 10980, 12726, 13500, 13842, 14130, 14670, 15120, 15210, 16170, 16368, 18000, 18018, 19170, 19710, 20040, 20400, 20538, 20790

Offset

1,1

Links

Table of n, a(n) for n=1..38.

Formula

Positive integers n such that A195860(n) = 9.

Example

180^1 = 180 is a multiple of Sum_digits(180) = 9;
180^2 = 32400 is a multiple of Sum_digits(32400) = 9;
180^3 = 5832000 is a multiple of Sum_digits(5832000) = 18;
180^4 = 1049760000 is a multiple of Sum_digits(1049760000) = 27;
180^5 = 188956800000 is a multiple of Sum_digits(188956800000) = 45;
180^6 = 34012224000000 is a multiple of Sum_digits(34012224000000) = 18;
180^7 = 6122200320000000 is a multiple of Sum_digits(6122200320000000) = 18;
180^8 = 1101996057600000000 is a multiple of Sum_digits(1101996057600000000) = 45;
180^9 = 198359290368000000000 is not a multiple of Sum_digits(198359290368000000000) = 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(10000, 8);

Crossrefs

Cf. A135186, A135187, A135188, A135189, A135190, A135191, A135192, A135194, A135195, A135196, A135197, A135198, A135199, A135200, A135201, A135202.

Sequence in context: A350372 A179643 A160134 * A095650 A066164 A008891

Adjacent sequences: A135190 A135191 A135192 * A135194 A135195 A135196

Keyword

nonn,base

Author

Paolo P. Lava & Giorgio Balzarotti, Nov 23 2007

Extensions

More terms from Max Alekseyev, Sep 24 2011

Status

approved