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A115374 Least prime p such that sigma(x)=sigma(p) has exactly n solutions. 2


%S 2,11,23,179,71,167,239,431,359,503,3167,1511,4679,2687,719,9719,4799,

%T 16319,5471,10559,1439,26399,24623,3359,15359,3023,7559,6719,2879,

%U 26783,10799,13103,5039,6047,45863,29759,61559,18719,27647,99839,22679,68543

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

%C 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.

%H Donovan Johnson, <a href="/A115374/b115374.txt">Table of n, a(n) for n = 1..1199</a>

%t 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}]]

%o (PARI) sigv(n) = select(i->sigma(i) == n, vector(n, i, i));

%o a(n) = {p = 2; while (#(sigv(p+1))! = n, p = nextprime(p+1)); p;} \\ _Michel Marcus_, May 01 2014

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

%K nonn

%O 1,1

%A _T. D. Noe_, Jan 21 2006

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