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A036690
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Product of a prime and the following number.
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10
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6, 12, 30, 56, 132, 182, 306, 380, 552, 870, 992, 1406, 1722, 1892, 2256, 2862, 3540, 3782, 4556, 5112, 5402, 6320, 6972, 8010, 9506, 10302, 10712, 11556, 11990, 12882, 16256, 17292, 18906, 19460, 22350, 22952, 24806, 26732, 28056, 30102
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OFFSET
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1,1
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COMMENTS
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The infinite sum over the reciprocals is given in A179119. - Wolfdieter Lang, Jul 10 2019
1/a(n) is the asymptotic density of numbers whose prime(n)-adic valuation is positive and even. - Amiram Eldar, Jan 23 2021
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..1000
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FORMULA
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a(n) = prime(n)*(prime(n)+1).
a(n) = A060800(n) - 1.
a(n) = 2*A034953(n). - Artur Jasinski, Feb 06 2007
From Amiram Eldar, Jan 23 2021: (Start)
Product_{n>=1} (1 + 1/a(n)) = zeta(2)/zeta(3) (A306633).
Product_{n>=1} (1 - 1/a(n)) = A065463. (End)
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EXAMPLE
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a(3)=30 because prime(3)=5 and prime(3)+1=6, hence 5*6 = 30.
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MATHEMATICA
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Table[(Prime[n] + 1) Prime[n], {n, 1, 100}] (* Artur Jasinski, Feb 06 2007 *)
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PROG
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(MAGMA)[p^2+p: p in PrimesUpTo(250)]; // Vincenzo Librandi, Dec 19 2010
(PARI) a(n)=my(p=prime(n)); p*(p+1) \\ Charles R Greathouse IV, Mar 27 2020
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CROSSREFS
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Cf. A036689, A034953, A065463, A179119, A306633.
Sequence in context: A071342 A125056 A011987 * A229746 A256579 A322374
Adjacent sequences: A036687 A036688 A036689 * A036691 A036692 A036693
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KEYWORD
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nonn,easy
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AUTHOR
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Felice Russo
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STATUS
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approved
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