|
Search: id:A114447
|
|
|
| A114447 |
|
Indices of 6-almost prime pentagonal numbers. |
|
+0
1
|
|
| 32, 48, 64, 72, 81, 82, 91, 99, 108, 112, 117, 123, 135, 139, 144, 152, 155, 160, 162, 176
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
P(2) = 5 is the only prime pentagonal number, all other factor as P(k) = (k/2)*(3*k-1) or k*((3*k-1)/2) and thus have at least 2 prime factors. P(k) is semiprime iff [k prime and (3*k-1)/2 prime] or [k/2 prime and 3*k-1 prime].
|
|
LINKS
|
Eric Weisstein's World of Mathematics, Pentagonal Number.
Eric Weisstein's World of Mathematics, Almost Prime.
|
|
FORMULA
|
{a(n)} = {k such that A001222(A000326(k)) = 6}. {a(n)} = {k such that k*(3*k-1)/2 has exactly 6 prime factors}. {a(n)} = {k such that A000326(k) is an element of A046306}.
|
|
EXAMPLE
|
a(1) = 32 because P(32) = PentagonalNumber(32) = 32*(3*32-1)/2 = 1520 = 2^4 * 5 * 19 is a 6-almost prime.
a(3) = 64 because P(64) = 64*(3*64-1)/2 = 6112 = 2^5 * 191 is a 6-almost
prime.
a(15) = 144 because P(144) = 144*(3*144-1)/2 = 31032 = 2^3 * 3^2 * 431 is a 6-almost prime.
|
|
CROSSREFS
|
Cf. A000326, A001222, A046306.
Sequence in context: A114406 A114416 A046304 this_sequence A090052 A036329 A014614
Adjacent sequences: A114444 A114445 A114446 this_sequence A114448 A114449 A114450
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
Jonathan Vos Post (jvospost3(AT)gmail.com), Feb 14 2006
|
|
|
Search completed in 0.002 seconds
|
