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A109315 Numbers n such that prime(n) - n is a prime power. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

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

FORMULA

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

EXAMPLE

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

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

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.

Sequence in context: A065150 A277082 A087098 * A024875 A152190 A079322

Adjacent sequences:  A109312 A109313 A109314 * A109316 A109317 A109318

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified October 20 01:39 EDT 2018. Contains 316378 sequences. (Running on oeis4.)