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 A325508 Product of primes indexed by the prime exponents of n!. 18
 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 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

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Last modified April 18 15:04 EDT 2021. Contains 343089 sequences. (Running on oeis4.)