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Search: id:A139807
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| A139807 |
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Number of distinct values of Product_{p is a part of P} (p-1) when P ranges over all partitions of n. |
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+0
1
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| 1, 2, 2, 3, 3, 5, 4, 8, 7, 11, 11, 17, 16, 25, 24, 35, 35, 50, 49, 70, 69, 94, 96, 129, 129, 172, 174, 227, 232, 298, 303, 389, 396, 498, 513, 639, 655, 814, 834, 1025, 1057, 1287, 1326, 1610, 1657, 1995, 2063, 2469, 2548, 3039, 3138, 3720, 3851, 4539, 4696, 5523
(list; graph; listen)
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OFFSET
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1,2
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LINKS
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Max Alekseyev, Proof of the conjecture
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FORMULA
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Conjecture: G.f. is x/(1-x)+((1-x^12)/((1-x^2)*(1-x^5)))*(1/Product_{k>0} (1-x^(prime(k)+1))), i.e. a(n) = 1 + number of partitions of n into parts of the form p+1, p a prime, excluding 12 and including 2 and 5. Added May 28 2008: The conjecture is correct! See the link. - Max Alekseyev (maxale(AT)gmail.com).
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MAPLE
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A139807 := proc(n) local g, i, p ; g := (1-x^12)/(1-x^2)/(1-x^5) ; for i from 1 do p := ithprime(i) ; if p > n then break ; fi ; g := taylor(g/(1-x^(p+1)), x=0, n+1) ; od: coeftayl( g+1/(1-x), x=0, n) ; end: seq(A139807(n), n=1..80) ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 29 2008
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CROSSREFS
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Cf. A034891.
Sequence in context: A036819 A114328 A097366 this_sequence A167755 A033302 A072729
Adjacent sequences: A139804 A139805 A139806 this_sequence A139808 A139809 A139810
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KEYWORD
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nonn
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AUTHOR
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Vladeta Jovovic (vladeta(AT)eunet.rs), May 23 2008
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 29 2008
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