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 A135199 Numbers n that raised to the powers from 1 to k (with k>=1) are multiples of the sum of their digits (and n raised to k+1 must not be such a multiple). Case k=14. 12
 60, 150, 600, 1500, 3390, 4320, 6000, 9240, 15000, 33900, 43200, 51810, 60000, 92400, 150000, 288750, 339000, 432000, 518100, 600000, 612150, 686070, 794640, 924000, 1043460, 1122450, 1225350, 1305150, 1483020, 1500000, 1711710, 2125620, 2174970 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS FORMULA Positive integers n such that A195860(n)=15. EXAMPLE 60^1=60 is multiple of Sum_digits(60)=6 60^2=3600 is multiple of Sum_digits(3600)=9 ... 60^14=7836416409600000000000000 is a multiple of Sum_digits(7836416409600000000000000)=54 while 60^15=470184984576000000000000000 is not multiple of Sum_digits(470184984576000000000000000)=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(30000, 14); MATHEMATICA msdQ[n_]:=Module[{b=Boole[Divisible[#, Total[IntegerDigits[#]]]&/@(n^Range[ 15])]}, Total[b]==14&&Last[b]==0]; Select[Range[22*10^5], msdQ] (* Harvey P. Dale, Apr 07 2019 *) CROSSREFS Cf. A135186, A135187, A135188, A135189, A135190, A135191, A135192, A135193, A135194, A135195, A135196, A135197, A135198, A135200, A135201, A135202. Sequence in context: A039497 A218243 A218392 * A112065 A252018 A044392 Adjacent sequences:  A135196 A135197 A135198 * A135200 A135201 A135202 KEYWORD nonn,base AUTHOR Paolo P. Lava and Giorgio Balzarotti, Nov 26 2007 EXTENSIONS Terms a(10) onward from Max Alekseyev, Sep 24 2011 Definition clarified by Harvey P. Dale, Apr 07 2019 STATUS approved

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Last modified April 18 12:34 EDT 2021. Contains 343087 sequences. (Running on oeis4.)