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Search: id:A067688
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| A067688 |
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Composite n such that for some integer r, n equals the sum of the r-th powers of the prime factors of n (counted with multiplicity). |
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+0
3
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| 4, 16, 27, 256, 3125, 19683, 65536, 823543, 1096744, 2836295, 4294967296, 4473671462
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Every prime is the sum of the first powers of its prime factors, so only composite numbers have been considered in this sequence.
Every integer of the form p^p^k with p prime and k>0 is in the sequence, since it equals the sum of the (p^k - k)-th powers of its prime factors. The first 8 terms of the sequence are of this form, but 1096744 = 2^3*11^3*103 and 2836295 = 5*7*11*53*139 are not.
4473671462=2*13*179*593*1621 is also not a prime power.
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EXAMPLE
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The sum of the cubes of the prime factors of 1096744 is 3*2^3 + 3*11^3 + 103^3 = 1096744.
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MATHEMATICA
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For[n=2, True, n++, If[ !PrimeQ[n], For[r=1; fn=FactorInteger[n]; s=0, s<=n, r++, s=Plus@@((#[[2]]#[[1]]^r)&/@fn); If[s==n, Print[{n, r}]]]]]
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CROSSREFS
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Cf. A068916, A081177 (for values of r).
Sequence in context: A072653 A008478 A111260 this_sequence A046358 A046366 A097374
Adjacent sequences: A067685 A067686 A067687 this_sequence A067689 A067690 A067691
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KEYWORD
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nonn
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AUTHOR
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Joseph L. Pe (joseph_l_pe(AT)hotmail.com), Feb 04 2002
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EXTENSIONS
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Edited by Dean Hickerson (dean.hickerson(AT)yahoo.com), Mar 07 2002
More terms from Jud McCranie (j.mccranie(AT)comcast.net), Mar 10 2003
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