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

Author

Felice Russo

Keywords

• nonn
• easy

Comments

Records in A002618. - Artur Jasinski, Jan 23 2008

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

Examples

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

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Index to sequences related to prime powers

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.

Programs

Haskell

a036689 n = a036689_list !! (n-1)
a036689_list = zipWith (*) a000040_list $ map pred a000040_list
-- Reinhard Zumkeller, Sep 17 2011

Magma

[ n*(n-1): n in PrimesUpTo(220) ]; // Bruno Berselli, Apr 11 2011

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 *)

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

Scheme

(define (A036689 n) (* (A000040 n) (- (A000040 n) 1))) ;; Antti Karttunen, May 01 2015

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)

Extensions

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