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A203521
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a(n) = Product_{1 <= i < j <= n} (prime(i) + prime(j)).
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5
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1, 1, 5, 280, 302400, 15850598400, 32867800842240000, 5539460271229108224000000, 55190934927547677562078494720000000, 61965661927377302817151474643396198400000000000, 14512955968670787590604912803260278557019929051136000000000000
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OFFSET
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0,3
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COMMENTS
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Each term divides its successor, as in A203511. It is conjectured that each term is divisible by the corresponding superfactorial, A000178(n). See A093883 for a guide to related sequences.
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LINKS
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EXAMPLE
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a(1) = 1.
a(2) = 2 + 3 = 5.
a(3) = (2+3)(2+5)(3+5) = 280.
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MAPLE
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a:= n-> mul(mul(ithprime(i)+ithprime(j), i=1..j-1), j=2..n):
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MATHEMATICA
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f[j_] := Prime[j]; z = 15;
v[n_] := Product[Product[f[k] + f[j], {j, 1, k - 1}], {k, 2, n}]
d[n_] := Product[(i - 1)!, {i, 1, n}] (* A000178 *)
Table[v[n], {n, 1, z}] (* A203521 *)
Table[v[n + 1]/v[n], {n, 1, z - 1}] (* A203522 *)
Table[v[n]/d[n], {n, 1, 20}] (* A203523 *)
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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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