|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
|