

A115374


Least prime p such that sigma(x)=sigma(p) has exactly n solutions.


2



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

1,1


COMMENTS

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.


LINKS



MATHEMATICA

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}]]


PROG

(PARI) sigv(n) = select(i>sigma(i) == n, vector(n, i, i));
a(n) = {p = 2; while (#(sigv(p+1))! = n, p = nextprime(p+1)); p; } \\ Michel Marcus, May 01 2014


CROSSREFS

Cf. A007368 (least k such that sigma(x)=k has n solutions), A066075 (number of solutions to sigma(x)=sigma(prime(n))).


KEYWORD

nonn


AUTHOR



STATUS

approved



