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A036689 Product of a prime and the previous number. 50
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Records in A002618. - Artur Jasinski, Jan 23 2008

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

Order Galois Field GF[p^2] where p are successive primes. - Artur Jasinski, Jul 04 2010

Maximal possible order of solvable transitive Galois group for polynomials of p degree. - Artur Jasinski, Feb 27 2011

LINKS

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

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

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 *)

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

(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, A053650, A053192, A053193, A053650, A117495.

Twice the terms of A008837.

Subsequence of A002378 (oblong numbers).

Column 1 of A257251. (Row 1 of A257252).

Sequence in context: A087150 A214307 A087134 * A226326 A139115 A193538

Adjacent sequences:  A036686 A036687 A036688 * A036690 A036691 A036692

KEYWORD

nonn,easy

AUTHOR

Felice Russo

STATUS

approved

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Last modified June 27 11:25 EDT 2017. Contains 288788 sequences.