login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A123118 Partial products of A101695. 0
2, 12, 216, 8640, 933120, 209018880, 100329062400, 130026464870400, 349511137571635200, 1968446726803449446400, 22676506292775737622528000, 522466704985552994823045120000, 27820307107070725868337506549760000 (list; graph; refs; listen; history; text; internal format)
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 * A182161 A165950 A208651

Adjacent sequences:  A123115 A123116 A123117 * A123119 A123120 A123121

KEYWORD

nonn

AUTHOR

Jonathan Vos Post, Sep 28 2006

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 17 13:29 EDT 2021. Contains 348049 sequences. (Running on oeis4.)