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A125136
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Triangle read by rows in which row n gives list of prime factors of p^p + 1 where p = prime(n).
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5
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5, 2, 2, 7, 2, 3, 521, 2, 2, 2, 113, 911, 2, 2, 3, 23, 89, 199, 58367, 2, 7, 13417, 20333, 79301, 2, 3, 3, 45957792327018709121, 2, 2, 5, 108301, 1049219, 870542161121, 2, 2, 2, 3, 47, 139, 1013, 1641281, 52626071, 1522029233, 2, 3, 5, 233, 6864997
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OFFSET
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1,1
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COMMENTS
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Product over the n-th row of the table is A051674(n) + 1. The number of elements in the n-th row is A115973(n). - R. J. Mathar, Jan 22 2007
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LINKS
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EXAMPLE
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Rows read
5;
2, 2, 7;
2, 3, 521;
2, 2, 2, 113, 911;
2, 2, 3, 23, 89, 199, 58367;
2, 7, 13417, 20333, 79301;
2, 3, 3, 45957792327018709121;
2, 2, 5, 108301, 1049219, 870542161121;
2, 2, 2, 3, 47, 139, 1013, 1641281, 52626071, 1522029233;
2, 3, 5, 233, 6864997, 9487923853, 5639663878716545087233;
2, 2, 2, 2, 2, 373, 1613, 62869, 145577, 35789156484227, 2706690202468649;
etc.
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MAPLE
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pfs := proc(n) local ifs, a, e, b ; ifs := ifactors(n)[2] ; a := [] ; for b from 1 to nops(ifs) do for e from 1 to op(2, op(b, ifs)) do a := [op(a), op(1, op(b, ifs))] ; od ; od ; RETURN(a) ; end; A125136 := proc(nmax) local a, p, n, pp ; a := [] ; p := 2 ; while nops(a) < nmax do a := [op(a), op(pfs(p^p+1))] ; p := nextprime(p) ; od ; RETURN(a) ; end; A125136(40) ; # R. J. Mathar, Jan 22 2007
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MATHEMATICA
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lpf[n_]:=Flatten[Table[#[[1]], #[[2]]]&/@FactorInteger[n]]; lpf/@(#^#+1&/@ Prime[Range[10]])//Flatten (* Harvey P. Dale, Oct 18 2020 *)
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CROSSREFS
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Cf. A007571 = largest factor of n^n + 1.
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KEYWORD
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nonn,tabf
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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