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A220849
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a(n) = Product_{d|n} Product_{d_x|n , d_x <= d} d_x.
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1
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1, 2, 3, 16, 5, 432, 7, 1024, 81, 2000, 11, 71663616, 13, 5488, 10125, 1048576, 17, 816293376, 19, 2048000000, 27783, 21296, 23, 219122084616339456, 625, 35152, 59049, 15420489728, 29, 2550916800000000000, 31, 34359738368, 107811, 78608, 214375
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OFFSET
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1,2
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COMMENTS
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Conjecture: sequence is injective (all terms of this sequence occur only once).
The subsequence of fixed points consists of 1 together with the primes (A008578). - Bernard Schott, Oct 26 2021
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LINKS
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FORMULA
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a(p) = p for prime p.
For p prime and k >= 0, a(p^k) = p^A000292(k).
For n = p*q, p < q primes (A006881), a(n) = p*n^3. (End)
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EXAMPLE
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The divisors of 6 are 1, 2, 3, 6. a(n) = 1*(1*2)*(1*2*3)*(1*2*3*6) = 1*2*6*36 = 432.
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MATHEMATICA
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a[n_] := Module[{d = Divisors[n], nd}, nd = Length[d]; Product[d[[i]]^(nd - i + 1), {i, 1, nd}]]; Array[a, 35] (* Amiram Eldar, Oct 23 2021 *)
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PROG
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(PARI) a(n) = my(d=divisors(n)); prod(k=1, #d, vecprod(select(x->(x<=d[k]), d))); \\ Michel Marcus, Oct 23 2021
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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