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A036689
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Product of a prime and the previous number.
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50
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2, 6, 20, 42, 110, 156, 272, 342, 506, 812, 930, 1332, 1640, 1806, 2162, 2756, 3422, 3660, 4422, 4970, 5256, 6162, 6806, 7832, 9312, 10100, 10506, 11342, 11772, 12656, 16002, 17030, 18632, 19182, 22052, 22650, 24492, 26406, 27722, 29756, 31862, 32580, 36290, 37056, 38612, 39402, 44310
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OFFSET
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1,1
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COMMENTS
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LINKS
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FORMULA
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a(n) = prime(n) * (prime(n) - 1).
a(n) = prime(n)! mod (prime(n)^2). - J. M. Bergot, Apr 10 2014
Product_{n>=1} (1 + 1/a(n)) = zeta(2)*zeta(3)/zeta(6) (A082695).
Product_{n>=1} (1 - 1/a(n)) = A005596. (End)
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EXAMPLE
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2*1, 3*2, 5*4, 7*6, 11*10, 13*12, 17*16, ...
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MAPLE
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A036689 := proc(n) local p ; p := ithprime(n) ; p*(p-1) ; end proc: # R. J. Mathar, Apr 11 2011
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MATHEMATICA
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Table[Prime[n] EulerPhi[Prime[n]], {n, 100}] (* Artur Jasinski, Jan 23 2008 *)
Table[Prime[n] (Prime[n] - 1), {n, 1, 50}] (* Bruno Berselli, Apr 22 2014 *)
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PROG
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(Magma) [ n*(n-1): n in PrimesUpTo(220) ]; // Bruno Berselli, Apr 11 2011
(Haskell)
a036689 n = a036689_list !! (n-1)
a036689_list = zipWith (*) a000040_list $ map pred a000040_list
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CROSSREFS
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Cf. A000040, A001248, A002618, A005596, A053650, A053192, A053193, A053650, A082695, A117495, A136141.
Subsequence of A002378 (oblong numbers).
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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