A114454 Numbers k such that the k-th hexagonal number is a 3-almost prime.

4, 5, 6, 9, 10, 11, 13, 15, 17, 21, 22, 29, 34, 43, 47, 49, 51, 55, 57, 61, 67, 69, 71, 73, 82, 87, 89, 91, 101, 103, 106, 107, 109, 115, 121, 127, 129, 141, 142, 151, 159, 166, 169, 177, 181, 187, 191, 197, 201, 205, 217, 223, 227, 241, 251, 262, 269, 274, 277, 283

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

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 A014612.

Numbers k such that A001222(A000384(k)) = 3.

Numbers k such that A001222(k*(2*k-1)) = 3.

Example

a(1) = 4 because HexagonalNumber(4) = H(4) = 4*(2*4-1) = 28 = 2^2 * 7 is a 3-almost prime.
a(2) = 5 because H(5) = 5*(2*5-1) = 45 = 3^2 * 5 is a 3-almost prime.
a(3) = 6 because H(6) = 6*(2*6-1) = 66 = 2 * 3 * 11 is a 3-almost prime.

Maple

A000384 := proc(n) n*(2*n-1) ; end: isA014612 := proc(n) option remember ; RETURN( numtheory[bigomega](n) = 3) ; end: for n from 1 to 400 do if isA014612(A000384(n)) then printf("%d, ", n) ; fi; od: # R. J. Mathar, Jan 27 2009

Mathematica

Select[Range[300], PrimeOmega[PolygonalNumber[6, #]] == 3 &] (* Amiram Eldar, Oct 06 2024 *)

Crossrefs

Cf. A000384, A001222, A014612.

Sequence in context: A029776 A064931 A177103 * A008854 A062726 A159629

Adjacent sequences: A114451 A114452 A114453 * A114455 A114456 A114457

Keyword

easy,nonn

Author

Jonathan Vos Post, Feb 14 2006

Extensions

151 to 177 inserted and extended by R. J. Mathar, Jan 27 2009

Status

approved