A113609 Number of prime powers q<=n such that also q+2 is a prime power.

1, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 16

Offset: 1

Author

Reinhard Zumkeller, Jan 14 2006

Keywords

• nonn

Comments

a(n) > A071538(n);

(25,27) is the smallest pair of prime powers (q,q+2) such that both q and q+2 are not primes, conjecture: there are more (but not < 10^6).

Examples

			a(10) = Card{(p^0,3), (2,2^2), (3,5), (5,7), (7,3^2), (3^2,11)} = 6.
		

Links

• Eric Weisstein's World of Mathematics, Prime Power
• Index entries for sequences related to numbers of primes in various ranges

Crossrefs

Cf. A000961, A071538.

Programs

PARI

ispp(n) = (n==1) || isprimepower(n);
a(n) = sum(k=1, n, ispp(k) && ispp(k+2)); \\ Michel Marcus, Jun 24 2019