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Search: id:A130680
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| A130680 |
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Numbers n such that n = (a_1 + a_2 + ... + a_p)*(a_1^3 + a_2^3 + ... + a_p^3), where n has the decimal expansion a_1a_2...a_p. |
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+0
1
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OFFSET
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1,2
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COMMENT
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This sequence is finite and all the terms are listed. Proof. Let a_1a_2...a_p be the decimal expansion of n. Then p <= log_10(n)+1. Furthermore we have a_i <= 9, therefore (a_1 + a_2 + ... + a_p) <= 9*(log_10(n)+1) and (a_1^3 + a_2^3 + ... + a_p^3) <= 9^3*(log_10(n)+1). On the other hand, for all n > 300000 we have 9^4*(log_10(n)+1)^2 < n. A computer search confirms that we indeed have found all terms.
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EXAMPLE
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87949=(8+7+9+4+9)*(8^3+7^3+9^3+4^3+9^3)
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MATHEMATICA
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For[n = 1, n < 1000000, n++, b = IntegerDigits[n]; If[Sum[b[[i]], {i, 1, Length[b]}] * Sum[b[[i]]^3, {i, 1, Length[b]}] == n, Print[n]]]
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CROSSREFS
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Cf. A115518.
Sequence in context: A047627 A047626 A105311 this_sequence A068783 A059287 A059669
Adjacent sequences: A130677 A130678 A130679 this_sequence A130681 A130682 A130683
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KEYWORD
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base,fini,full,nonn
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AUTHOR
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Aktar Yalcin (aktaryalcin(AT)msn.com), Jun 29 2007
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EXTENSIONS
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Edited by Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Jul 13 2007
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