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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.
1
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
1,1
FORMULA
a(n)=Card{x; Pi[x]-Pi[x/2]=n}, where Pi()=A000720().
EXAMPLE
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}.
CROSSREFS
Cf. A104272 Ramanujan primes. [From Jonathan Sondow, Aug 10 2008]
Sequence in context: A129531 A298264 A014476 * A365781 A298400 A070295
KEYWORD
nonn
AUTHOR
Labos Elemer, Feb 21 2003
EXTENSIONS
Definition corrected by Jonathan Sondow, Aug 10 2008
STATUS
approved