A115374 Least prime p such that sigma(x)=sigma(p) has exactly n solutions.

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

Offset: 1

Author

T. D. Noe, Jan 21 2006

Keywords

• nonn

Comments

For 11? 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

• Donovan Johnson, Table of n, a(n) for n = 1..1199

Crossrefs

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

Programs

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}]]

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