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Search: id:A068916
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| A068916 |
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Smallest positive integer that is equal to the sum of the n-th powers of its prime factors (counted with multiplicity). |
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+0
2
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OFFSET
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1,1
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COMMENT
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Does a(n) exist for all n?
a(12)=65536, a(27)=4394967296. a(n) exists for all n of the form n=p^i-i, where p is prime and i >= 0, since p^p^i is an example (see A067688 and A081177). - Jud McCranie (j.mccranie(AT)comcast.net), Mar 16 2003
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EXAMPLE
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a(3) = 1096744 = 2^3*11^3*103; the sum of the cubes of the prime factors is 3*2^3 + 3*11^3 + 103^3 = 1096744.
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MATHEMATICA
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a[n_] := For[x=1, True, x++, If[x==Plus@@(#[[2]]#[[1]]^n&/@FactorInteger[x]), Return[x]]]
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CROSSREFS
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Cf. A067688.
Cf. A081177, A000325, A024024, A024050.
Sequence in context: A088321 A061301 A092798 this_sequence A093987 A114560 A108883
Adjacent sequences: A068913 A068914 A068915 this_sequence A068917 A068918 A068919
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KEYWORD
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nonn
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AUTHOR
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Dean Hickerson (dean.hickerson(AT)yahoo.com), Mar 07 2002
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