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

1,1

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

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

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))).

Sequence in context: A342185 A217309 A378697 * A078699 A291679 A239741

Adjacent sequences: A115371 A115372 A115373 * A115375 A115376 A115377

Keyword

nonn

Author

T. D. Noe, Jan 21 2006

Status

approved