A109919 a(1) = 1, then product of consecutive composite numbers sandwiched between primes.

1, 2, 1, 3, 4, 5, 6, 7, 720, 11, 12, 13, 3360, 17, 18, 19, 9240, 23, 11793600, 29, 30, 31, 45239040, 37, 59280, 41, 42, 43, 91080, 47, 311875200, 53, 549853920, 59, 60, 61, 1072431360, 67, 328440, 71, 72, 73, 2533330800, 79, 531360, 83, 4701090240, 89

Offset: 1

Author

Amarnath Murthy, Jul 16 2005

Keywords

• easy
• nonn

Comments

a(1) = a(3) = 1 as empty product is defined to be 1.

The odd numbered terms are in A061214. - T. D. Noe, Oct 02 2012

Crossrefs

Cf. A109920.

Cf. A072472.

Cf. A061214 (product of composite numbers between primes).

Programs

Maple

A109919 := proc(n) local p; if n mod 2 = 0 then ithprime(n/2) ; elif n = 1 then 1 ; else p := ithprime((n-1)/2) ; mul(i,i=p+1..nextprime(p)-1) ; fi ; end: for n from 1 to 80 do printf("%d, ",A109919(n)) ; od ; # R. J. Mathar, May 02 2007

Formula

a(2n) = prime(n) and a(2n+1)= product of composite numbers between prime(n) and prime(n+1).

a(2n) = A000040(n). a(2n+1) = A072472(n)/A000040(n+1). - R. J. Mathar, May 02 2007

Extensions

More terms from R. J. Mathar, May 02 2007