A036689 Product of a prime and the previous number.

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

Offset

1,1

Comments

Records in A002618. - Artur Jasinski, Jan 23 2008

Also records in A174857. - Vladimir Shevelev, Mar 31 2010

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Index to sequences related to prime powers

Formula

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)

Example

2*1, 3*2, 5*4, 7*6, 11*10, 13*12, 17*16, ...

Maple

A036689 := proc(n) local p ; p := ithprime(n) ; p*(p-1) ; end proc: # R. J. Mathar, Apr 11 2011

Mathematica

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 *)

Prog

(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
(PARI) A036689(n) = ((p->(p-1)*p)(prime(n))); \\ Antti Karttunen, Dec 14 2024
(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

Crossrefs

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.)

Column 2 of A379010.

Sequence in context: A087134 A378027 A370494 * A355390 A226326 A139115

Adjacent sequences: A036686 A036687 A036688 * A036690 A036691 A036692

Keyword

nonn,easy

Author

Felice Russo

Extensions

Deleted two incorrect comments. - N. J. A. Sloane, May 07 2020

Status

approved