

A113609


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


0



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
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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



