

A114456


Numbers n such that the nth hexagonal number is a 5almost prime.


0



8, 14, 16, 18, 20, 24, 28, 36, 38, 40, 41, 44, 54, 74, 77, 78, 84, 86, 90, 92, 100, 102, 105, 110, 113, 123, 124, 125, 126, 130, 132, 135, 136, 143, 148, 149, 153, 156, 164, 165, 170, 171, 184, 185, 186, 194, 207, 210, 213, 215, 218, 220, 225, 232, 234, 236
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OFFSET

1,1


COMMENTS

There are no prime hexagonal numbers. The nth hexagonal number A000384(n) = n*(2*n1) is semiprime iff both n and 2*n1 are prime iff A000384(n) is an element of A001358 iff n is an element of A005382.


LINKS

Table of n, a(n) for n=1..56.
Eric Weisstein's World of Mathematics, Hexagonal Number.
Eric Weisstein's World of Mathematics, Almost Prime.


FORMULA

n such that hexagonal number A000384(n) is an element of A014614. n such that A001222(A000384(n)) = 5. n such that A001222(n*(2*n1)) = 5.


EXAMPLE

a(1) = 8 because HexagonalNumber(8) = H(8) = 8*(2*81) = 120 = 2^3 * 3 * 5 is a 5almost prime.
a(2) = 14 because H(14) = 14*(2*141) = 378 = 2 * 3^3 * 7 is a 5almost prime.
a(3) = 18 because H(18) = 18*(2*181) = 630 = 2 * 3^2 * 5 * 7 is a 5almost prime.
a(20) = 100 because H(100) = 100*(2*1001) = 19900 = 2^2 * 5^2 * 199 is a 5almost prime.


MATHEMATICA

Select[Range[300], PrimeOmega[#*(2*#  1)] == 5 &] (* Giovanni Resta, Jun 14 2016 *)


CROSSREFS

Cf. A000384, A001222, A014614.
Sequence in context: A082772 A103338 A250004 * A230422 A050681 A292867
Adjacent sequences: A114453 A114454 A114455 * A114457 A114458 A114459


KEYWORD

easy,nonn


AUTHOR

Jonathan Vos Post, Feb 14 2006


EXTENSIONS

Missing a(3)=16 and more terms from Giovanni Resta, Jun 14 2016


STATUS

approved



