A109315 Numbers n such that prime(n) - n is a prime power.

12, 15, 38, 39, 118, 152, 190, 258, 462, 690, 746, 1396, 1632, 2119, 3370, 4522, 4600, 7520, 15006, 24222, 33156, 34038, 51372, 52342, 64638, 77470, 90790, 101946, 104670, 156772, 166822, 167700, 175818, 194092, 200022, 229630, 246208, 328462, 362440, 372882

Offset: 1

Author

Zak Seidov and Robert G. Wilson v, May 22 2005

Keywords

• nonn

Examples

			690 is OK because prime(690)-690 = 5179-690 = 4489 = 67^2, 67 is prime.
		

Links

• Donovan Johnson, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A025475 = powers of a prime but not prime, also nonprime n such that sigma(n)*phi(n)>(n-1)2; A107712 = values of q, A107713 = values of k; A107714 = values of prime(A109315(n)).

Cf. A083240.

Programs

Mathematica

lst = {}; fQ[n_] := Block[{pf=FactorInteger[n]}, (2-Length[pf])(pf[[1, 2]]-1) > 0]; Do[ If[ fQ[Prime[n] - n], Print[n]; AppendTo[lst, n]], {n, 3, 362439}]; lst

Formula

prime(n) - n = q^k, q is prime and k_Integer >= 2.