A135190 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=5.

3, 12, 36, 42, 102, 162, 432, 468, 1002, 1026, 1080, 1188, 1215, 1380, 1512, 1620, 1770, 1950, 1980, 2136, 2394, 2460, 2466, 2628, 3210, 3240, 3276, 3492, 3540, 3654, 3816, 3864, 4032, 4050, 4116, 4374, 4680, 4752, 4806, 4860, 4950, 5058, 5238

Offset

1,1

Links

Table of n, a(n) for n=1..43.

Formula

Positive integers n such that A195860(n)=6.

Example

3^1=3
3^2=9 and 9 is a multiple of 3
3^3=27 -> Sum_digits(27)=9 and 27 is a multiple of 9
3^4=81 -> Sum_digits(81)=9 and 81 is a multiple of 9
3^5=243 -> Sum_digits(243)=9 and 243 is a multiple of 9
3^6=729 -> Sum_digits(729)=18 and 729 is not a multiple of 18

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, 5);

Crossrefs

Cf. A135186, A135187, A135188, A135189, A135191, A135192, A135193, A135194, A135195, A135196, A135197, A135198, A135199, A135200, A135201, A135202.

Sequence in context: A305542 A232899 A009787 * A101069 A225259 A334891

Adjacent sequences: A135187 A135188 A135189 * A135191 A135192 A135193

Keyword

nonn,base

Author

Paolo P. Lava & Giorgio Balzarotti, Nov 22 2007

Extensions

More terms from Max Alekseyev, Sep 24 2011

Status

approved