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A220027 a(n) = product(i >= 0, P(n, i)^(2^i)) where P(n, i) = product(p prime, n/2^(i+1) < p <= n/2^i). 1
1, 1, 2, 6, 12, 60, 180, 1260, 5040, 5040, 25200, 277200, 2494800, 32432400, 227026800, 227026800, 3632428800, 61751289600, 61751289600, 1173274502400, 29331862560000, 29331862560000, 322650488160000, 7420961227680000, 601097859442080000, 601097859442080000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(n) are the partial products of A219964(n).

a(n) divides n!, n!/a(n) = 1, 1, 1, 1, 2, 2, 4, 4, 8, 72, 144, 144, 192...

The swinging factorial (A056040) divides a(n), a(n)/n$ = 1, 1, 1, 1, 2,...

The primorial of n (A034386) divides a(n), a(n)/n# = 1, 1, 1, 1, 2, 2, 6,..

If p^k is the largest power of a prime dividing a(n) then k is 2^n for some n >= 0.

a(n) / A055773(n) is the largest square dividing a(n), a(n) / A055773(n) = A008833(a(n)).

LINKS

Table of n, a(n) for n=0..25.

MAPLE

a := proc(n) local k; `if`(n < 2, 1,

mul(k, k = select(isprime, [$iquo(n, 2)+1..n]))*a(iquo(n, 2))^2) end:

seq(a(i), i=0..25);

PROG

(Sage)

def a(n) :

    if n < 2 : return 1

    return mul(k for k in prime_range(n//2+1, n+1))*a(n//2)^2

[a(n) for n in (0..25)]

CROSSREFS

Cf. A055773.

Sequence in context: A101657 A104371 A104350 * A072489 A072487 A254232

Adjacent sequences:  A220024 A220025 A220026 * A220028 A220029 A220030

KEYWORD

nonn

AUTHOR

Peter Luschny, Mar 30 2013

STATUS

approved

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Last modified February 18 20:32 EST 2018. Contains 299330 sequences. (Running on oeis4.)