A114455 Numbers k such that the k-th hexagonal number is a 4-almost prime.

12, 23, 25, 26, 27, 30, 33, 35, 39, 42, 45, 46, 52, 53, 58, 59, 62, 65, 66, 70, 75, 76, 83, 85, 93, 94, 99, 111, 114, 117, 118, 119, 131, 133, 134, 137, 145, 146, 147, 154, 155, 161, 163, 167, 173, 174, 175, 178, 179, 183, 190, 193, 195, 202, 206, 209, 214, 219, 222, 226, 231, 233, 235, 237, 239

Offset

1,1

Comments

There are no prime hexagonal numbers. The k-th hexagonal number A000384(k) = k*(2*k-1) is semiprime iff both k and 2*k-1 are primes iff A000384(k) is an element of A001358 iff k is an element of A005382.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)

Eric Weisstein's World of Mathematics, Almost Prime.

Eric Weisstein's World of Mathematics, Hexagonal Number.

Formula

Numbers k such that hexagonal number A000384(k) is an element of A014613.

Numbers k such that A001222(A000384(k)) = 4.

Numbers k such that A001222(k*(2*k-1)) = 4.

Example

a(1) = 12 because HexagonalNumber(12) = H(12) = 12*(2*12-1) = 276 = 2^2 * 3 * 23 is a 4-almost prime.
a(2) = 23 because H(23) = 23*(2*23-1) = 1035 = 3^2 * 5 * 23 is a 4-almost prime.
a(3) = 25 because H(25) = 25*(2*25-1) = 1225 = 5^2 * 7^2 is a 4-almost prime.

Mathematica

Select[Range[250], PrimeOmega[#(2#-1)]==4&] (* Harvey P. Dale, Feb 18 2013 *)

Crossrefs

Cf. A000384, A001222, A014613.

Sequence in context: A246342 A101104 A330212 * A048992 A088783 A029756

Adjacent sequences: A114452 A114453 A114454 * A114456 A114457 A114458

Keyword

easy,nonn

Author

Jonathan Vos Post, Feb 14 2006

Extensions

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

Status

approved