

A182910


Number of unitary prime divisors of the swinging factorial (A056040) n$ = n! / floor(n/2)!^2.


1



0, 0, 1, 2, 2, 3, 1, 2, 3, 3, 1, 2, 3, 4, 3, 3, 4, 5, 4, 5, 4, 6, 5, 6, 5, 5, 4, 4, 3, 4, 5, 6, 7, 8, 6, 6, 7, 8, 7, 7, 8, 9, 9, 10, 9, 7, 6, 7, 7, 7, 7, 8, 7, 8, 8, 10, 11, 13, 12, 13, 11, 12, 11, 10, 11, 13, 12, 13
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OFFSET

0,4


COMMENTS

A prime divisor of n is unitary iff its exponent is 1 in the prime power factorization of n. A unitary prime divisor of the swinging factorial n$ can be smaller than n/2. For n >= 30 the swinging factorial has more unitary prime divisors than the factorial and it has never less unitary prime divisors. Thus a(n) >= PrimePi(n)  PrimePi(n/2).


LINKS

Table of n, a(n) for n=0..67.


EXAMPLE

16$ = 2.3.3.5.11.13. So 16$ has one nonunitary prime divisor and a(16) = 4.


MAPLE

UnitaryPrimeDivisor := proc(f, n) local k, F; F := f(n):
add(`if`(igcd(iquo(F, k), k)=1, 1, 0), k=numtheory[factorset](F)) end;
A056040 := n > n!/iquo(n, 2)!^2;
A182910 := n > UnitaryPrimeDivisor(A056040, n);
seq(A182910(i), i=1..LEN);


CROSSREFS

Cf. A056171.
Sequence in context: A226743 A166269 A181648 * A055460 A067514 A115323
Adjacent sequences: A182907 A182908 A182909 * A182911 A182912 A182913


KEYWORD

nonn


AUTHOR

Peter Luschny, Mar 14 2011


STATUS

approved



