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A071963
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Largest prime factor of p(n), the n-th partition number A000041(n) (with a(0) = a(1) = 1 by convention).
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9
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1, 1, 2, 3, 5, 7, 11, 5, 11, 5, 7, 7, 11, 101, 5, 11, 11, 11, 11, 7, 19, 11, 167, 251, 7, 89, 29, 43, 13, 83, 467, 311, 23, 23, 1231, 41, 17977, 281, 43, 11, 127, 193, 2417, 71, 97, 1087, 241, 67, 7013, 631, 9283, 661, 53, 5237, 59, 227, 1019, 102359, 3251, 199, 409, 971
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OFFSET
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0,3
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COMMENTS
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Cilleruelo and Luca prove that a(n) > log log n, for almost all n.
By computation, a(n) > log n, at least up to n = 2500. In fact, a(n) > n if n > 39, at least up to n = 2500; see A192885. - Jonathan Sondow, Aug 16 2011
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LINKS
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FORMULA
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EXAMPLE
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MATHEMATICA
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Table[First[Last[FactorInteger[PartitionsP[n]]]], {n, 0, 100}] (* Jonathan Sondow, Aug 16 2011 *)
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PROG
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(PARI) for(n=2, 75, print1(vecmax(component(factor(polcoeff(1/eta(x), n, x)), 1)), ", "))
(PARI) a(n)=local(v); if(n<2, n>=0, v=factor(polcoeff(1/eta(x+x*O(x^n)), n))~[1, ]; v[ #v])
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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