A135568 -id:A135568 - cp's OEIS frontend

A182254 a(n) = primorial(n) mod n!.

0, 0, 0, 0, 18, 30, 510, 1470, 22890, 284550, 3171630, 18486930, 45347610, 4254260010, 2349577230, 371965003410, 9252750236730, 190224835871070, 221717289063270, 14855058367239090, 1662934646118135390, 45974266913148043470, 4510191947325194130

Offset: 0

Alex Ratushnyak, Apr 21 2012

nonn

a(n) mod 6 = 0 and a(n) mod 30 = 0, n<>4. - Gary Detlefs, May 02 2012

			a(5) = (2*3*5*7*11) mod (1*2*3*4*5) = 2310 mod 120 = 30.

Harvey P. Dale, Table of n, a(n) for n = 0..449

Cf. A002110, A000142, A000040, A135568.

primorial[n_] := Product[Prime[i], {i, n}]; Table[Mod[primorial[n], n!], {n, 0, 30}] (* T. D. Noe, Apr 21 2012 *)
With[{nn=30},Join[{0},Mod[#[[2]],#[[1]]]&/@Transpose[{Range[nn]!, FoldList[ Times, Prime[Range[nn]]]}]]] (* Harvey P. Dale, May 26 2016 *)

a(n) = A002110(n) mod A000142(n).

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

Original entry on oeis.org

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

Ilya Gutkovskiy, Apr 06 2016

			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.

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

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

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

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

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)).

cp's OEIS Frontend

A182254 a(n) = primorial(n) mod n!.

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