A325508 Product of primes indexed by the prime exponents of n!.

1, 1, 2, 4, 10, 20, 42, 84, 204, 476, 798, 1596, 3828, 7656, 12276, 24180, 36660, 73320, 120840, 241680, 389424, 785680, 1294440, 2588880, 3848880, 7147920, 11264760, 15926040, 26057304, 52114608, 74421648, 148843296, 187159392, 340949280, 527531760, 926505360

Offset: 0

Author

Gus Wiseman, May 08 2019

Keywords

• nonn

Comments

The prime indices of a(n) are the signature of n!, which is row n of A115627.

Examples

			We have 7! = 2^4 * 3^2 * 5^1 * 7^1, so a(7) = prime(4)*prime(2)*prime(1)*prime(1) = 84.
The sequence of terms together with their prime indices begins:
          1: {}
          1: {}
          2: {1}
          4: {1,1}
         10: {1,3}
         20: {1,1,3}
         42: {1,2,4}
         84: {1,1,2,4}
        204: {1,1,2,7}
        476: {1,1,4,7}
        798: {1,2,4,8}
       1596: {1,1,2,4,8}
       3828: {1,1,2,5,10}
       7656: {1,1,1,2,5,10}
      12276: {1,1,2,2,5,11}
      24180: {1,1,2,3,6,11}
      36660: {1,1,2,3,6,15}
      73320: {1,1,1,2,3,6,15}
     120840: {1,1,1,2,3,8,16}
     241680: {1,1,1,1,2,3,8,16}
		

Crossrefs

Cf. A000142, A011371, A022559, A056171, A071626, A076934, A115627, A118914, A122111, A135291, A181819, A307035, A323014, A325272, A325273, A325276, A325509.

Programs

Mathematica

Table[Times@@Prime/@Last/@If[(n!)==1,{},FactorInteger[n!]],{n,0,30}]

Formula

a(n) = A181819(n!).

A001221(a(n)) = A071626(n).

A001222(a(n)) = A000720(n).

A056239(a(n)) = A022559(n).

A003963(a(n)) = A135291(n).

A061395(a(n)) = A011371(n).

A007814(a(n)) = A056171(n).

a(n) = A122111(A307035(n)). - Antti Karttunen, Nov 19 2019