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A285634
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a(1) = 4, a(n) = Product_{d|a(n-1)} d.
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0
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OFFSET
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1,1
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COMMENTS
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Iterating the product-of-divisors function.
The next term is too large to include.
Let a(n) = Product_{d|a(n-1)} d, with a(1) = p^k, p is a prime, k >= 0 and b(n) = b(n-1)*(b(n-1) + 1)/2, with b(1) = k, then a(n) = p^b(n).
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LINKS
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FORMULA
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a(1) = 4, a(n) = a(n-1)^(A000005(a(n-1))/2).
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EXAMPLE
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a(1) = 4;
a(2) = 8 because 4 has 3 divisors {1, 2, 4} and 1*2*4 = 8;
a(3) = 64 because 64 has 7 divisors {1, 2, 4, 8, 16, 32, 64} and 1*2*4*8*16*32*64 = 2097152, etc.
...
a(6) = 2^26796;
a(7) = 2^359026206;
a(8) = 2^64449908476890321;
a(9) = 2^2076895351339769460477611370186681, etc.
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MATHEMATICA
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RecurrenceTable[{a[1] == 4, a[n] == Sqrt[a[n - 1]]^DivisorSigma[0, a[n - 1]]}, a, {n, 5}]
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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