A123118 Partial products of A101695.

2, 12, 216, 8640, 933120, 209018880, 100329062400, 130026464870400, 349511137571635200, 1968446726803449446400, 22676506292775737622528000, 522466704985552994823045120000, 27820307107070725868337506549760000

Offset

1,1

Comments

The number of prime factors (with multiplicity) of a(n) is T(n) = A000217(n) = n*(n+1)/2.

Links

Table of n, a(n) for n=1..13.

Formula

a(n) = Prod[i=1..n] i-th i-almost prime = Prod[i=1..n] A101695(i).

Example

a(1) = 2 = prime(1).
a(2) = 12 = 2 * 6 = prime(1) * semiprime(2) = 2^2 * 3.
a(3) = 216 = 2 * 6 * 18 = prime(1) * semiprime(2) * 3-almostprime(3) = 2^3 * 3^3.
a(4) = 8640 = 2 * 6 * 18 * 40 = prime(1) * semiprime(2) * 3-almostprime(3) * 4-almostprime(4) = 2^6 * 3^3 * 5.
a(15) = 893179304874387947794472921245209518407680000 = 2 * 6 * 18 * 40 * 108 * 224 * 480 * 1296 * 2688 * 5632 * 11520 * 23040 * 53248 * 124416 * 258048 = 2^88 * 3^23 * 5^4 * 7^3 * 11 * 13.

Crossrefs

Cf. A000040, A001358, A014612, A014613, A046314, A046306, A046308, A046310, A046312, A046314, A069272, A069273, A069274, A069275, A069276, A069277, A069278, A069279, A069280, A069281, A101637, A101638, A101605, A101606, A101695.

Sequence in context: A082491 A292812 A153302 * A367051 A182161 A165950

Adjacent sequences: A123115 A123116 A123117 * A123119 A123120 A123121

Keyword

nonn

Author

Jonathan Vos Post, Sep 28 2006

Status

approved