A080361 a(n) is the difference between the largest and the smallest positive integers x such that the number of unitary-prime-divisors of x! equals n. Same as the difference between the largest and the smallest positive integers x such that the number of primes in (x/2,x] equals n.

8, 13, 15, 21, 15, 15, 13, 9, 25, 27, 5, 23, 39, 37, 27, 21, 7, 45, 37, 39, 39, 1, 21, 17, 11, 35, 27, 53, 35, 17, 19, 27, 29, 9, 11, 11, 5, 21, 43, 27, 11, 69, 61, 63, 15, 5, 1, 5, 33, 29, 27, 5, 5, 17, 57, 43, 47, 17, 25, 51, 47, 11, 3, 25, 27, 23, 77, 57, 35, 19, 29, 37, 27, 23, 9

Offset: 1

Author

Labos Elemer, Feb 21 2003

Keywords

• nonn

Links

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

Crossrefs

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

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

Formula

a(n)=Max{x; Pi[x]-Pi[x/2]=n}-Min{x; Pi[x]-Pi[x/2]=n}=A080360[n]-A080359[n].

Extensions

Definition corrected by Jonathan Sondow, Aug 10 2008

Typo in formula corrected by Daniel Forgues, Aug 06 2009