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Search: id:A135191
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| A135191 |
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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=6. |
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+0
17
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| 24, 54, 510, 540, 624, 690, 888, 960, 1110, 1530, 1710, 1848, 2010, 2070, 2142, 2232, 2604, 2844, 2916
(list; graph; listen)
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OFFSET
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1,1
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EXAMPLE
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24^1=24 -> Sum_digits(24)=6 and 24 is a multiple of 6.
24^2=576 -> Sum_digits(576)=18 and 576 is a multiple of 18.
24^3=13824 -> Sum_digits(13824)=18 and 13824 is a multiple of 18.
24^4=331776 -> Sum_digits(331776)=27 and 331776 is a multiple of 27.
24^5=7962624 -> Sum_digits(7962624)=36 and 7962624 is a multiple of 36.
24^6=191102976 -> Sum_digits(191102976)=36 and 191102976 is a multiple of 36.
24^7=4586471424 -> Sum_digits(4586471424)=45 and 4586471424 is not a multiple of 45.
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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, 6);
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CROSSREFS
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Cf. A135186, A135187, A135188, A135189, A135190, A135192, A135193, A135194, A135195, A135196, A135197, A135198, A135199, A135200, A135201, A135202.
Sequence in context: A038635 A005782 A003756 this_sequence A039375 A043198 A043978
Adjacent sequences: A135188 A135189 A135190 this_sequence A135192 A135193 A135194
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KEYWORD
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easy,nonn,base
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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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