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A135192
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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=7.
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14
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126, 480, 660, 810, 882, 1020, 1134, 1170, 1260, 1320, 1560, 1590, 2022, 3042, 3222, 4662, 4800, 5670, 5940, 6240, 6600, 7110, 7452, 8100, 8442, 8550, 8820, 8880, 9510, 10110, 10200, 10350, 10620, 10890, 11010, 11106, 11130, 11340, 11460, 11700, 11970
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OFFSET
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1,1
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LINKS
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FORMULA
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Positive integers n such that A195860(n) = 8.
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EXAMPLE
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126^1 = 126 -> Sum_digits(126) = 9, and 126 is a multiple of 9
126^2 = 15876 -> Sum_digits(15876) = 27, and 15876 is a multiple of 27
126^3 = 2000376 -> Sum_digits(2000376) = 18, and 2000376 is a multiple of 18
126^4 = 252047376 -> Sum_digits(252047376) = 36, and 252047376 is a multiple of 36
126^5 = 31757969376 -> Sum_digits(31757969376) = 63, and 31757969376is a multiple of 63
126^6 = 4001504141376 -> Sum_digits(4001504141376) = 36, and 4001504141376 is a multiple of 36
126^7 = 504189521813376 -> Sum_digits(504189521813376) = 63, and 504189521813376 is a multiple of 63
126^8 = 63527879748485376 -> Sum_digits(63527879748485376) = 99, and 63527879748485376 is not a multiple of 99
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MAPLE
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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, 7);
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MATHEMATICA
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msdQ[n_]:=AllTrue[n^Range[7], Divisible[#, Total[IntegerDigits[#]]]&] && !Divisible[n^8, Total[IntegerDigits[n^8]]]; Select[Range[12000], msdQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Apr 01 2017 *)
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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