A135186 Numbers n that raised to the powers from 1 to k (with k>=1) are multiples of the sums of their digits (and n raised to the power k+1 is not such a multiple). Case k=1.

4, 5, 7, 8, 27, 40, 50, 70, 81, 114, 133, 135, 152, 153, 171, 192, 195, 209, 222, 224, 225, 228, 230, 247, 261, 266, 280, 285, 308, 312, 320, 322, 336, 364, 370, 372, 375, 392, 399, 400, 405, 407, 408, 410, 423, 440, 444, 448, 465, 481, 500, 511, 512, 516, 518

Offset

1,1

Comments

The sequence is a subset of Niven (or Harshad) numbers A005349.

Links

Table of n, a(n) for n=1..55.

Formula

Positive integers n such that A195860(n) = 2.

Example

7 can be divided only for 7^1; 7^2 = 49, sum_digits(49) = 13, and 49 is not a multiple of 13.

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, 1);

Crossrefs

Cf. A135187 - A135202.

Sequence in context: A226628 A335842 A140076 * A011336 A094328 A081095

Adjacent sequences: A135183 A135184 A135185 * A135187 A135188 A135189

Keyword

nonn,base

Author

Paolo P. Lava & Giorgio Balzarotti, Nov 22 2007

Extensions

Definition edited by N. J. A. Sloane, Sep 04 2010

Status

approved