A135195 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=10.

6, 330, 360, 1230, 1440, 2250, 2490, 2970, 3150, 3300, 3600, 4410, 5010, 5310, 6930, 8460, 10020, 12300, 12840, 12852, 13050, 14400, 14700, 15420, 15840, 16500, 17220, 18480, 20010, 21840, 22500, 23310, 24840, 24900, 27702, 28050, 29610, 29700, 31500

Offset

1,1

Links

Table of n, a(n) for n=1..39.

Formula

Positive integers n such that A195860(n)=11.

Example

6^1=6 is a multiple of Sum_digits(6)=6
6^2=36 is a multiple of Sum_digits(36)=9
6^3=216 is a multiple of Sum_digits(216)=9
6^4=1296 is a multiple of Sum_digits(1296)=18
6^5=7776 is a multiple of Sum_digits(7776)=27
6^6=46656 is a multiple of Sum_digits(46656)=27
6^7=279936 is a multiple of Sum_digits(279936)=36
6^8=1679616 is a multiple of Sum_digits(1679616)=36
6^9=10077696 is a multiple of Sum_digits(10077696)=36
6^10=60466176 is a multiple of Sum_digits(60466176)=36
6^11=362797056 is not a multiple of Sum_digits(362797056)=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(15000, 10);

Crossrefs

Cf. A135186, A135187, A135188, A135189, A135190, A135191, A135192, A135193, A135194, A135196, A135197, A135198, A135199, A135200, A135201, A135202.

Sequence in context: A221884 A003742 A324099 * A273031 A358485 A001509

Adjacent sequences: A135192 A135193 A135194 * A135196 A135197 A135198

Keyword

nonn,base

Author

Paolo P. Lava and Giorgio Balzarotti, Nov 23 2007

Extensions

Example corrected by Paolo P. Lava, Oct 23 2009

More terms from Max Alekseyev, Sep 24 2011

Status

approved