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.
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
KEYWORD
nonn
AUTHOR
T. D. Noe, Nov 09 2009
STATUS
approved
