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A036689
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Product of a prime and the previous number.
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43
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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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refs;
listen;
history;
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OFFSET
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1,1
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COMMENTS
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Records in A002618. - Artur Jasinski, Jan 23 2008
Also records in A174857. - Vladimir Shevelev, Mar 31 2010
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LINKS
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Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Index to sequences related to prime powers
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FORMULA
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a(n) = prime(n) * (prime(n) - 1).
a(n) = phi(prime(n)^2) = A000010(A001248(n)).
a(n) = prime(n) * phi(prime(n)). - Artur Jasinski, Jan 23 2008
From Reinhard Zumkeller, Sep 17 2011: (Start)
a(n) = A000040(n) * A006093(n) = A001248(n) - A000040(n).
A006530(a(n)) = A000040(n). (End)
a(n) = A009262(prime(n)). - Enrique Pérez Herrero, May 12 2012
a(n) = prime(n)! mod (prime(n)^2). - J. M. Bergot, Apr 10 2014
a(n) = 2* A008837(n). - Antti Karttunen, May 01 2015
Sum_{n>=1} 1/a(n) = A136141. - Amiram Eldar, Nov 09 2020
From Amiram Eldar, Jan 23 2021: (Start)
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 *)
#(#-1)&/@Prime[Range[50]] (* Harvey P. Dale, Sep 08 2019 *)
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PROG
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(MAGMA) [ n*(n-1): n in PrimesUpTo(220) ]; // Bruno Berselli, Apr 11 2011
(PARI) forprime(p=2, 1e3, print1(p^2-p", ")) \\ Charles R Greathouse IV, Jun 10 2011
(Haskell)
a036689 n = a036689_list !! (n-1)
a036689_list = zipWith (*) a000040_list $ map pred a000040_list
-- Reinhard Zumkeller, Sep 17 2011
(Scheme) (define (A036689 n) (* (A000040 n) (- (A000040 n) 1))) ;; Antti Karttunen, May 01 2015
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CROSSREFS
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Cf. A000040, A001248, A002618, A005596, A053650, A053192, A053193, A053650, A082695, A117495, A136141.
Twice the terms of A008837.
Subsequence of A002378 (oblong numbers).
Column 1 of A257251. (Row 1 of A257252.)
Sequence in context: A323724 A214307 A087134 * A226326 A139115 A193538
Adjacent sequences: A036686 A036687 A036688 * A036690 A036691 A036692
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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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EXTENSIONS
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Deleted two incorrect comments. - N. J. A. Sloane, May 07 2020
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STATUS
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approved
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