A080362 a(n) is the number of positive integers x such that the number of unitary-prime-divisors of x! equals n. Same as the number of positive integers x such that the number of primes in (x/2,x] equals n.

4, 10, 7, 14, 7, 10, 12, 5, 14, 16, 3, 10, 18, 16, 15, 11, 7, 16, 19, 14, 9, 2, 14, 14, 8, 11, 18, 19, 24, 10, 14, 16, 20, 10, 11, 3, 6, 13, 18, 21, 9, 31, 37, 10, 15, 6, 2, 6, 21, 12, 7, 6, 6, 16, 15, 34, 14, 10, 15, 29, 22, 9, 4, 14, 16, 17, 25, 36, 12, 15, 13, 19, 19, 8, 10, 5, 12

Offset: 1

Author

Labos Elemer, Feb 21 2003

Keywords

• nonn

Examples

			n=5,a(5)=7 because in 7 factorials 5 primes arise with exponent 1: in factorials of 31,32,33,37,41,46; e.g. in 37! these are {19,23,29,31,37}, or 10 numbers x, exist such ones that number of unitary prime divisors of x! equals 2, namely in factorials of {3,5,7,8,9,11,12,13,15,16}.
		

Links

• J. Sondow, Ramanujan Prime in MathWorld [From _Jonathan Sondow_, Aug 10 2008]

Crossrefs

Cf. A056171, A056169, A000720, A000142, A080359, A080360, A080361.

Cf. A104272 Ramanujan primes. [From Jonathan Sondow, Aug 10 2008]

Formula

a(n)=Card{x; Pi[x]-Pi[x/2]=n}, where Pi()=A000720().

Extensions

Definition corrected by Jonathan Sondow, Aug 10 2008