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A114445 Indices of 5-almost prime pentagonal numbers. 0
11, 35, 40, 42, 51, 54, 59, 63, 67, 80, 87, 92, 100, 115, 120, 125, 126, 131, 132, 136, 159, 165, 167, 168, 175 (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..25.

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)) = 5}. {a(n)} = {k such that k*(3*k-1)/2 has exactly 5 prime factors}. {a(n)} = {k such that A000326(k) is an element of A014614}.

EXAMPLE

a(1) = 11 because P(11) = PentagonalNumber(11) = 11*(3*11-1)/2 = 176 = 2^4 * 11 is a 4-almost prime (the prime factors need not be distinct).

a(2) = 35 because P(35) = 35*(3*35-1)/2 = 1820 = 2^2 * 5 * 7 * 13 is a 5-almost

prime.

a(13) = 100 because P(100) = 100*(3*100-1)/2 = 14950 = 2 * 5^2 * 13 * 23 is a 5-almost

prime.

CROSSREFS

Cf. A000326, A001222, A014614.

Sequence in context: A050287 A096762 A184207 * A054475 A029540 A319971

Adjacent sequences:  A114442 A114443 A114444 * A114446 A114447 A114448

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, Feb 14 2006

STATUS

approved

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Last modified August 20 10:41 EDT 2019. Contains 326150 sequences. (Running on oeis4.)