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A036690 Product of a prime and the following number. 10

%I

%S 6,12,30,56,132,182,306,380,552,870,992,1406,1722,1892,2256,2862,3540,

%T 3782,4556,5112,5402,6320,6972,8010,9506,10302,10712,11556,11990,

%U 12882,16256,17292,18906,19460,22350,22952,24806,26732,28056,30102

%N Product of a prime and the following number.

%C The infinite sum over the reciprocals is given in A179119. - _Wolfdieter Lang_, Jul 10 2019

%C 1/a(n) is the asymptotic density of numbers whose prime(n)-adic valuation is positive and even. - _Amiram Eldar_, Jan 23 2021

%H Vincenzo Librandi, <a href="/A036690/b036690.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = prime(n)*(prime(n)+1).

%F a(n) = A060800(n) - 1.

%F a(n) = 2*A034953(n). - _Artur Jasinski_, Feb 06 2007

%F From _Amiram Eldar_, Jan 23 2021: (Start)

%F Product_{n>=1} (1 + 1/a(n)) = zeta(2)/zeta(3) (A306633).

%F Product_{n>=1} (1 - 1/a(n)) = A065463. (End)

%e a(3)=30 because prime(3)=5 and prime(3)+1=6, hence 5*6 = 30.

%t Table[(Prime[n] + 1) Prime[n], {n, 1, 100}] (* _Artur Jasinski_, Feb 06 2007 *)

%o (MAGMA)[p^2+p: p in PrimesUpTo(250)]; // _Vincenzo Librandi_, Dec 19 2010

%o (PARI) a(n)=my(p=prime(n)); p*(p+1) \\ _Charles R Greathouse IV_, Mar 27 2020

%Y Cf. A036689, A034953, A065463, A179119, A306633.

%K nonn,easy

%O 1,1

%A _Felice Russo_

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Last modified April 13 22:53 EDT 2021. Contains 342941 sequences. (Running on oeis4.)