|
Search: id:A123118
|
|
| |
|
| 2, 12, 216, 8640, 933120, 209018880, 100329062400, 130026464870400, 349511137571635200, 1968446726803449446400, 22676506292775737622528000, 522466704985552994823045120000, 27820307107070725868337506549760000
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
The number of prime factors (with multiplicity) of a(n) is T(n) = A000217(n) = n*(n+1)/2.
|
|
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: A008352 A082491 A153302 this_sequence A165950 A083667 A092124
Adjacent sequences: A123115 A123116 A123117 this_sequence A123119 A123120 A123121
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Jonathan Vos Post (jvospost3(AT)gmail.com), Sep 28 2006
|
|
|
Search completed in 0.003 seconds
|
