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A167675 Least prime p such that p-2 has n divisors, or 0 if no such prime exists. 0
3, 5, 11, 17, 83, 47, 0, 107, 227, 569, 59051, 317, 0, 9479, 2027, 947, 0, 2207, 0, 2837, 88211, 295247, 0, 3467, 50627, 9034499, 11027, 47387, 0, 14177, 0, 15017, 1476227, 215233607, 455627, 17327, 150094635296999123, 15884240051, 89813531, 36857, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This sequence is the idea of Alonso Del Arte. For n>2, a(n) is conjectured to be the smallest number that is orderly (see A167408) for n-1 values of k. For example, 11 is orderly for k=3 and 9. See A056899 for other primes p that are orderly for two k. It is a conjecture because it is not known whether there are composite numbers that are orderly for more than one value of k.

The terms a(n) for prime n are 0 except when 3^(n-1)+2 is prime. Using A051783, we find the exceptional primes to be n=2, 3, 5, 11, 37, 127, 6959.... For these n, a(n) = 3^(n-1)+2. For any n, it is easy to use the factorization of n to find the forms of numbers that have n divisors. For example, for n=38=2*19, we know that the prime must have the form 2+q*r^18 with q and r prime. The smallest such prime is 2+41*3^18.

LINKS

Table of n, a(n) for n=1..41.

MATHEMATICA

nn=25; t=Table[0, {nn}]; Do[p=Prime[n]; k=DivisorSigma[0, p-2]; If[k<=nn && t[[k]]==0, t[[k]]=p], {n, 2, 10^6}]; t

CROSSREFS

Cf. A066814 (smallest prime p such that p-1 has n divisors)

Sequence in context: A078883 A155990 A109556 * A277284 A090952 A270778

Adjacent sequences:  A167672 A167673 A167674 * A167676 A167677 A167678

KEYWORD

nonn

AUTHOR

T. D. Noe, Nov 09 2009

STATUS

approved

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Last modified April 11 11:17 EDT 2021. Contains 342886 sequences. (Running on oeis4.)