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

1,2

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).

Links

Table of n, a(n) for n=1..77.

Eric Weisstein's World of Mathematics, Prime Power

Index entries for sequences related to numbers of primes in various ranges

Example

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

Prog

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

Crossrefs

Cf. A000961, A071538.

Sequence in context: A024745 A322921 A030581 * A206916 A336112 A067086

Adjacent sequences: A113606 A113607 A113608 * A113610 A113611 A113612

Keyword

nonn

Author

Reinhard Zumkeller, Jan 14 2006

Status

approved