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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
Sequence in context: A039497 A218243 A218392 * A112065 A252018 A044392
KEYWORD
nonn,base
AUTHOR
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 22 08:00 EDT 2024. Contains 371892 sequences. (Running on oeis4.)