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Search: id:A115374
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| A115374 |
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Least prime p such that sigma(x)=sigma(p) has exactly n solutions. |
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+0
2
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| 2, 11, 23, 179, 71, 167, 239, 431, 359, 503, 3167, 1511, 4679, 2687, 719, 9719, 4799, 16319, 5471, 10559, 1439, 26399, 24623, 3359, 15359, 3023, 7559, 6719, 2879, 26783, 10799, 13103, 5039, 6047, 45863, 29759, 61559, 18719, 27647, 99839, 22679, 68543
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OFFSET
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1,1
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COMMENT
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For 1<n<258, we have a(n)=11 (mod 12). Is this true for all n>1? It also appears that for each n there are an infinite number of primes p such that sigma(x)=sigma(p) has exactly n solutions.
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MATHEMATICA
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s=DivisorSigma[1, Range[100000]]; t=Table[Length[Position[s, Prime[n]+1]], {n, PrimePi[Length[s]]}]; u=Union[t]; nLast=First[Complement[Range[u[[ -1]]], u]]-1; Flatten[Table[Prime[Position[t, n, 1, 1]], {n, nLast}]]
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CROSSREFS
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Cf. A007368 (least k such that sigma(x)=k has n solutions), A066075 (number of solutions to sigma(x)=sigma(prime(n))).
Sequence in context: A090424 A141423 A106974 this_sequence A078699 A042347 A041803
Adjacent sequences: A115371 A115372 A115373 this_sequence A115375 A115376 A115377
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KEYWORD
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nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Jan 21 2006
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