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Search: id:A135192
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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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+0
17
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| 126, 480, 660, 810, 882, 1020, 1134, 1170, 1260, 1320, 1560, 1590, 2022, 3042, 3222
(list; graph; listen)
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OFFSET
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1,1
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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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CROSSREFS
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Cf. A135186, A135187, A135188, A135189, A135190, A135191, A135193, A135194, A135195, A135196, A135197, A135198, A135199, A135200, A135201, A135202.
Adjacent sequences: A135189 A135190 A135191 this_sequence A135193 A135194 A135195
Sequence in context: A109024 A063334 A102805 this_sequence A107658 A004008 A126170
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KEYWORD
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easy,nonn
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AUTHOR
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Paolo P. Lava & Giorgio Balzarotti (ppl(AT)spl.at), Nov 22 2007
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