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Search: id:A066075
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| A066075 |
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Number of solutions x to prime(n) = Sigma(x) - 1, where prime(n) is the n-th prime. |
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+0
3
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| 1, 1, 1, 1, 2, 1, 2, 1, 3, 1, 2, 1, 3, 1, 3, 2, 3, 1, 1, 5, 1, 2, 3, 3, 2, 1, 2, 2, 1, 2, 2, 2, 1, 2, 1, 2, 1, 1, 6, 1, 4, 2, 5, 1, 1, 1, 1, 3, 3, 1, 3, 7, 1, 6, 1, 2, 3, 2, 1, 1, 1, 3, 2, 4, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 1, 6, 2, 1, 1, 1, 4, 1, 8, 4, 2, 2, 3, 1, 1, 1, 3, 9, 1, 2, 1, 10, 1, 2, 1, 1
(list; graph; listen)
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OFFSET
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1,5
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COMMENT
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prime(n) itself is always the largest solution, but often composite solutions also occur.
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LINKS
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Harry J. Smith, Table of n, a(n) for n=1,...,1000
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EXAMPLE
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If a(n)=1, then the single solution is prime(n); n=96, p(96)=503, 503=sigma[x]-1 has 10 solutions together with 503: {204, 220, 224, 246, 284, 286, 334, 415, 451, 503} so a(96)=10.
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PROGRAM
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(PARI) { for (n=1, 1000, a=1; for (x=1, prime(n) - 1, if (prime(n) == (sigma(x) - 1), a++)); write("b066075.txt", n, " ", a) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Nov 10 2009]
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CROSSREFS
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Number of solutions to A000040(n)=A000203(x)-1
Cf. A000040, A000203, A066071-A066080.
Sequence in context: A161506 A066451 A091090 this_sequence A072347 A136107 A124768
Adjacent sequences: A066072 A066073 A066074 this_sequence A066076 A066077 A066078
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Dec 03 2001
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