login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Please make a donation to keep the OEIS running. In 2018 we replaced the server with a faster one, added 20000 new sequences, and reached 7000 citations (often saying "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A114447 Indices of 6-almost prime pentagonal numbers. 0
32, 48, 64, 72, 81, 91, 99, 108, 112, 117, 123, 135, 139, 144, 152, 155, 160, 162, 176, 195, 207, 208, 216, 219, 240, 252, 264, 272, 275, 279, 292, 297, 300 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

Table of n, a(n) for n=1..33.

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: A271784 A114416 A046304 * A090052 A163285 A036329

Adjacent sequences:  A114444 A114445 A114446 * A114448 A114449 A114450

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, Feb 14 2006

EXTENSIONS

82 removed by R. J. Mathar, Dec 22 2010

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 December 12 23:01 EST 2018. Contains 318081 sequences. (Running on oeis4.)