

A056171


Pi(n)pi(floor(n/2)), where pi is A000720.


14



0, 1, 2, 1, 2, 1, 2, 2, 2, 1, 2, 2, 3, 2, 2, 2, 3, 3, 4, 4, 4, 3, 4, 4, 4, 3, 3, 3, 4, 4, 5, 5, 5, 4, 4, 4, 5, 4, 4, 4, 5, 5, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 6, 7, 7, 8, 7, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 10, 9, 9, 9, 9, 9, 10, 10, 10, 9, 10, 10, 10, 9, 9, 9, 10, 10, 10, 10, 10, 9, 9, 9, 10, 10
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OFFSET

1,3


COMMENTS

Also, the number of unitary prime divisors of n!. A prime divisor of n is unitary iff its exponent is 1 in the prime power factorization of n. In general GCD(p, n/p) = 1 or p. Here we count the cases when GCD(p, n/p)=1.
A unitary prime divisor of n! is >= n/2, hence their number is pi(n)pi(n/2). [Peter Luschny, Mar 13 2011].
See also the references and links mentioned in A143227. [From Jonathan Sondow, Aug 03 2008]


LINKS

Daniel Forgues, Table of n, a(n) for n=1..100000


EXAMPLE

10!=2.2.2.2.2.2.2.2.3.3.3.3.5.5.7 The only unitary prime divisor is 7, so a(10)=1, while 10! has 3 nonunitary prime divisors.


MAPLE

with(numtheory); [seq(pi(n)pi(floor(n/2)), n=1..130)]; # from N. J. A. Sloane, Sep 01 2015
A056171 := n > nops(select(isprime, [$iquo(n, 2)+1..n])):
seq(A056171(i), i=1..98);  Peter Luschny, Mar 13 2011


MATHEMATICA

s=0; Table[If[PrimeQ[k], s++]; If[PrimeQ[k/2], s]; s, {k, 100}]
Table[PrimePi[n]PrimePi[Floor[n/2]], {n, 100}] (* Harvey P. Dale, Sep 01 2015 *)


CROSSREFS

Cf. A001221, A034444, A000720, A048105, A048656, A048657.
Cf. A014085, A060715, A104272, A143223, A143224, A143225, A143226, A143227. [From Jonathan Sondow, Aug 03 2008]
Sequence in context: A163377 A163109 A128428 * A238949 A076755 A106490
Adjacent sequences: A056168 A056169 A056170 * A056172 A056173 A056174


KEYWORD

nonn,easy


AUTHOR

Labos Elemer, Jul 27 2000


EXTENSIONS

Simplified definition.  N. J. A. Sloane, Sep 01 2015


STATUS

approved



