A080362 - OEIS

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

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OFFSET

1,1

LINKS

Table of n, a(n) for n=1..77.

J. Sondow, Ramanujan Prime in MathWorld [From Jonathan Sondow, Aug 10 2008]

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

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

Sequence in context: A129531 A298264 A014476 * A365781 A298400 A070295

Adjacent sequences: A080359 A080360 A080361 * A080363 A080364 A080365

KEYWORD

nonn

AUTHOR

Labos Elemer, Feb 21 2003

EXTENSIONS

Definition corrected by Jonathan Sondow, Aug 10 2008

STATUS

approved