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

1,2

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

Links

Table of n, a(n) for n=1..48.

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

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

Crossrefs

Cf. A109920.

Cf. A072472.

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

Sequence in context: A058684 A226054 A109920 * A345903 A346786 A239469

Adjacent sequences: A109916 A109917 A109918 * A109920 A109921 A109922

Keyword

easy,nonn

Author

Amarnath Murthy, Jul 16 2005

Extensions

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

Status

approved