A135191 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=6.

24, 54, 510, 540, 624, 690, 888, 960, 1110, 1530, 1710, 1848, 2010, 2070, 2142, 2232, 2604, 2844, 2916, 4020, 4230, 4332, 4488, 4968, 5100, 5202, 5280, 5400, 5550, 5742, 6420, 6444, 6630, 6636, 6660, 6900, 7350, 7920, 8190, 8592, 8610, 8730

Offset

1,1

Links

Table of n, a(n) for n=1..42.

Formula

Positive integers n such that A195860(n)=7.

Example

24^1 = 24 -> Sum_digits(24) = 6, and 24 is a multiple of 6.
24^2 = 576 -> Sum_digits(576) = 18, and 576 is a multiple of 18.
24^3 = 13824 -> Sum_digits(13824) = 18, and 13824 is a multiple of 18.
24^4 = 331776 -> Sum_digits(331776) = 27, and 331776 is a multiple of 27.
24^5 = 7962624 -> Sum_digits(7962624) = 36, and 7962624 is a multiple of 36.
24^6 = 191102976 -> Sum_digits(191102976) = 36, and 191102976 is a multiple of 36.
24^7 = 4586471424 -> Sum_digits(4586471424) = 45, and 4586471424 is not a multiple of 45.

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(2000, 6);

Crossrefs

Cf. A135186 - A135202.

Sequence in context: A351379 A038635 A003756 * A216697 A332541 A316361

Adjacent sequences: A135188 A135189 A135190 * A135192 A135193 A135194

Keyword

nonn,base

Author

Paolo P. Lava & Giorgio Balzarotti, Nov 22 2007

Extensions

More terms from Max Alekseyev, Sep 24 2011

Status

approved