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A325508
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Product of primes indexed by the prime exponents of n!.
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20
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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
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OFFSET
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0,3
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COMMENTS
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The prime indices of a(n) are the signature of n!, which is row n of A115627.
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LINKS
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FORMULA
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EXAMPLE
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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}
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MATHEMATICA
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Table[Times@@Prime/@Last/@If[(n!)==1, {}, FactorInteger[n!]], {n, 0, 30}]
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CROSSREFS
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Cf. A000142, A011371, A022559, A056171, A071626, A076934, A115627, A118914, A122111, A135291, A181819, A307035, A323014, A325272, A325273, A325276, A325509.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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