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A061742
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a(n) is the square of the product of first n primes.
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45
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1, 4, 36, 900, 44100, 5336100, 901800900, 260620460100, 94083986096100, 49770428644836900, 41856930490307832900, 40224510201185827416900, 55067354465423397733736100, 92568222856376731590410384100, 171158644061440576710668800200900
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OFFSET
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0,2
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COMMENTS
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Squares of primorials (first definition, A002110).
Exponential superabundant numbers: numbers k with a record value of the exponential abundancy index, A051377(k)/k > A051377(m)/m for all m < k. - Amiram Eldar, Apr 13 2019
Empirically, these are possibly the denominators for 1 - Sum_{k=1..n} (-1)^(k+1)/prime(k)^2. The numerators are listed in A136370. - Petros Hadjicostas, May 14 2020
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LINKS
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FORMULA
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EXAMPLE
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a(4) = 2^2 * 3^2 * 5^2 * 7^2 = 44100.
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MAPLE
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a:= proc(n) option remember; `if`(n=0, 1, ithprime(n)^2*a(n-1)) end:
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MATHEMATICA
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PROG
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(PARI) for(n=0, 20, print1(prod(k=1, n, prime(k)^2), ", "))
(PARI) { n=-1; m=1; forprime (p=2, prime(101), write("b061742.txt", n++, " ", m^2); m*=p ) } \\ Harry J. Smith, Jul 27 2009
(Magma) [n eq 0 select 1 else (&*[NthPrime(j)^2: j in [1..n]]): n in [0..20]]; // G. C. Greubel, Apr 19 2019
(Sage) [product(nth_prime(j)^2 for j in (1..n)) for n in (0..20)] # G. C. Greubel, Apr 19 2019
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CROSSREFS
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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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