This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A036690 #35 Mar 31 2025 14:18:42
%S A036690 6,12,30,56,132,182,306,380,552,870,992,1406,1722,1892,2256,2862,3540,
%T A036690 3782,4556,5112,5402,6320,6972,8010,9506,10302,10712,11556,11990,
%U A036690 12882,16256,17292,18906,19460,22350,22952,24806,26732,28056,30102
%N A036690 Product of a prime and the following number.
%C A036690 The infinite sum over the reciprocals is given in A179119. - _Wolfdieter Lang_, Jul 10 2019
%C A036690 1/a(n) is the asymptotic density of numbers whose prime(n)-adic valuation is positive and even. - _Amiram Eldar_, Jan 23 2021
%H A036690 Vincenzo Librandi, <a href="/A036690/b036690.txt">Table of n, a(n) for n = 1..1000</a>
%F A036690 a(n) = prime(n)*(prime(n)+1).
%F A036690 a(n) = A060800(n) - 1.
%F A036690 a(n) = 2*A034953(n). - _Artur Jasinski_, Feb 06 2007
%F A036690 From _Amiram Eldar_, Jan 23 2021: (Start)
%F A036690 Product_{n>=1} (1 + 1/a(n)) = zeta(2)/zeta(3) (A306633).
%F A036690 Product_{n>=1} (1 - 1/a(n)) = A065463. (End)
%F A036690 Sum_{n>=1} 1/a(n) = A179119. - _R. J. Mathar_, Mar 31 2025
%e A036690 a(3)=30 because prime(3)=5 and prime(3)+1=6, hence 5*6 = 30.
%t A036690 Table[(Prime[n] + 1) Prime[n], {n, 1, 100}] (* _Artur Jasinski_, Feb 06 2007 *)
%o A036690 (Magma)[p^2+p: p in PrimesUpTo(250)]; // _Vincenzo Librandi_, Dec 19 2010
%o A036690 (PARI) a(n)=my(p=prime(n)); p*(p+1) \\ _Charles R Greathouse IV_, Mar 27 2020
%Y A036690 Cf. A036689, A034953, A065463, A179119, A306633.
%K A036690 nonn,easy
%O A036690 1,1
%A A036690 _Felice Russo_