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%I #92 Sep 08 2022 08:44:52
%S 2,6,20,42,110,156,272,342,506,812,930,1332,1640,1806,2162,2756,3422,
%T 3660,4422,4970,5256,6162,6806,7832,9312,10100,10506,11342,11772,
%U 12656,16002,17030,18632,19182,22052,22650,24492,26406,27722,29756,31862,32580,36290,37056,38612,39402,44310
%N Product of a prime and the previous number.
%C Records in A002618. - _Artur Jasinski_, Jan 23 2008
%C Also records in A174857. - _Vladimir Shevelev_, Mar 31 2010
%H Reinhard Zumkeller, <a href="/A036689/b036689.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Pri#prime_powers">Index to sequences related to prime powers</a>
%F a(n) = prime(n) * (prime(n) - 1).
%F a(n) = phi(prime(n)^2) = A000010(A001248(n)).
%F a(n) = prime(n) * phi(prime(n)). - _Artur Jasinski_, Jan 23 2008
%F From _Reinhard Zumkeller_, Sep 17 2011: (Start)
%F a(n) = A000040(n) * A006093(n) = A001248(n) - A000040(n).
%F A006530(a(n)) = A000040(n). (End)
%F a(n) = A009262(prime(n)). - _Enrique Pérez Herrero_, May 12 2012
%F a(n) = prime(n)! mod (prime(n)^2). - _J. M. Bergot_, Apr 10 2014
%F a(n) = 2* A008837(n). - _Antti Karttunen_, May 01 2015
%F Sum_{n>=1} 1/a(n) = A136141. - _Amiram Eldar_, Nov 09 2020
%F From _Amiram Eldar_, Jan 23 2021: (Start)
%F Product_{n>=1} (1 + 1/a(n)) = zeta(2)*zeta(3)/zeta(6) (A082695).
%F Product_{n>=1} (1 - 1/a(n)) = A005596. (End)
%e 2*1, 3*2, 5*4, 7*6, 11*10, 13*12, 17*16, ...
%p A036689 := proc(n) local p ; p := ithprime(n) ; p*(p-1) ; end proc: # _R. J. Mathar_, Apr 11 2011
%t Table[Prime[n] EulerPhi[Prime[n]], {n, 100}] (* _Artur Jasinski_, Jan 23 2008 *)
%t Table[Prime[n] (Prime[n] - 1), {n, 1, 50}] (* _Bruno Berselli_, Apr 22 2014 *)
%t #(#-1)&/@Prime[Range[50]] (* _Harvey P. Dale_, Sep 08 2019 *)
%o (Magma) [ n*(n-1): n in PrimesUpTo(220) ]; // _Bruno Berselli_, Apr 11 2011
%o (PARI) forprime(p=2,1e3,print1(p^2-p", ")) \\ _Charles R Greathouse IV_, Jun 10 2011
%o (Haskell)
%o a036689 n = a036689_list !! (n-1)
%o a036689_list = zipWith (*) a000040_list $ map pred a000040_list
%o -- _Reinhard Zumkeller_, Sep 17 2011
%o (Scheme) (define (A036689 n) (* (A000040 n) (- (A000040 n) 1))) ;; _Antti Karttunen_, May 01 2015
%Y Cf. A000040, A001248, A002618, A005596, A053650, A053192, A053193, A053650, A082695, A117495, A136141.
%Y Twice the terms of A008837.
%Y Subsequence of A002378 (oblong numbers).
%Y Column 1 of A257251. (Row 1 of A257252.)
%K nonn,easy
%O 1,1
%A _Felice Russo_
%E Deleted two incorrect comments. - _N. J. A. Sloane_, May 07 2020
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