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

1,1

Links

Table of n, a(n) for n=1..75.

J. Sondow, Ramanujan Prime in MathWorld [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].

Crossrefs

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

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

Sequence in context: A271720 A243436 A214412 * A054295 A328241 A287159

Adjacent sequences: A080358 A080359 A080360 * A080362 A080363 A080364

Keyword

nonn

Author

Labos Elemer, Feb 21 2003

Extensions

Definition corrected by Jonathan Sondow, Aug 10 2008

Typo in formula corrected by Daniel Forgues, Aug 06 2009

Status

approved