A325508 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

A325508

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

20

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

COMMENTS

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

LINKS

Table of n, a(n) for n=0..35.

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

EXAMPLE

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}

MATHEMATICA

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

CROSSREFS

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

Sequence in context: A026644 A167193 A026666 * A238439 A121880 A094536

Adjacent sequences: A325505 A325506 A325507 * A325509 A325510 A325511

KEYWORD

nonn

AUTHOR

Gus Wiseman, May 08 2019

STATUS

approved