A271387 Numerator of prime(n)#/n!, where prime(n)# is the prime factorial function.

1, 2, 3, 5, 35, 77, 1001, 2431, 46189, 1062347, 30808063, 86822723, 3212440751, 10131543907, 435656388001, 20475850236047, 1085220062510491, 3766351981654057, 229747470880897477, 810162134158954261, 57521511525285752531, 4199070341345859934763, 331726556966322934846277

Offset

0,2

Links

Ilya Gutkovskiy, Table of n, a(n) for n = 0..75

Eric Weisstein's World of Mathematics, Primorial

Eric Weisstein's World of Mathematics, Prime Counting Function

Eric Weisstein's World of Mathematics, Factorial

Formula

a(n) = prime(n)#/GCD(prime(n)#, n!), where GCD(a, b) is the greatest common divisor.

a(n) = prime(n)#/prime(pi(n))#, where pi(n) is the number of primes <= n.

a(n) = A002110(n)/A034386(n) = A002110(n)/A002110(A000720(n)) = A002110(n)/A007947(A000142(n)).

Example

1, 2, 3, 5, 35/4, 77/4, 1001/24, 2431/24, 46189/192, 1062347/1728, 30808063/17280, 86822723/17280, 3212440751/207360, 10131543907/207360, 435656388001/2903040, ...
a(8) = 46189, because prime(8)#/8! = (2*3*5*7*11*13*17*19)/(1*2*3*4*5*6*7*8) = 46189/192.

Mathematica

Table[Numerator[Product[Prime@ k, {k, n}]/n!], {n, 0, 22}] (* Michael De Vlieger, Apr 08 2016 *)

Prog

(PARI) a(n) = numerator(prod(k=1, n, prime(k))/n!); \\ Michel Marcus, Apr 09 2016

Crossrefs

Cf. A000040, A000142, A000720, A002110, A007947, A034386, A049614 (denominator of prime(n)#/n!), A090586, A135568.

Sequence in context: A041977 A362640 A261130 * A089213 A029499 A347720

Adjacent sequences: A271384 A271385 A271386 * A271388 A271389 A271390

Keyword

nonn,frac

Author

Ilya Gutkovskiy, Apr 06 2016

Status

approved