A135194 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=9.

240, 270, 450, 630, 840, 1050, 2340, 2400, 2610, 2700, 3024, 3036, 3990, 4500, 5292, 6300, 6390, 8400, 9990, 10170, 10500, 17160, 18330, 23400, 24000, 26100, 27000, 30240, 30360, 31110, 35070, 39900, 40140, 40740, 41340, 41700, 43170, 43470, 44880

Offset

1,1

Links

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

Formula

Positive integers n such that A195860(n)=10.

Example

240^1=240 is a multiple of Sum_digits(240)=6.
240^2=57600 is a multiple of Sum_digits(240)=18.
240^3=13824000 is a multiple of Sum_digits(13824000)=18.
240^4=3317760000 is a multiple of Sum_digits(3317760000)=27.
240^5=796262400000 is a multiple of Sum_digits(796262400000)=36.
240^6=191102976000000 is a multiple of Sum_digits(191102976000000)=36.
240^7=45864714240000000 is a multiple of Sum_digits(45864714240000000)=45.
240^8=11007531417600000000 is a multiple of Sum_digits(11007531417600000000)=36.
240^9=2641807540224000000000 is a multiple of Sum_digits(2641807540224000000000)=45.
240^10=634033809653760000000000 is not a multiple of Sum_digits(634033809653760000000000)=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(15000, 9);

Crossrefs

Cf. A135186, A135187, A135188, A135189, A135190, A135191, A135192, A135193, A135195, A135196, A135197, A135198, A135199, A135200, A135201, A135202.

Sequence in context: A191533 A299527 A328589 * A031173 A067373 A291921

Adjacent sequences: A135191 A135192 A135193 * A135195 A135196 A135197

Keyword

nonn,base

Author

Paolo P. Lava and Giorgio Balzarotti, Nov 23 2007

Extensions

More terms from Max Alekseyev, Sep 24 2011

Status

approved