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A114456 Numbers n such that the n-th hexagonal number is a 5-almost 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

There are no prime hexagonal numbers. The n-th hexagonal number A000384(n) = n*(2*n-1) is semiprime iff both n and 2*n-1 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*n-1)) = 5.

EXAMPLE

a(1) = 8 because HexagonalNumber(8) = H(8) = 8*(2*8-1) = 120 = 2^3 * 3 * 5 is a 5-almost prime.

a(2) = 14 because H(14) = 14*(2*14-1) = 378 = 2 * 3^3 * 7 is a 5-almost prime.

a(3) = 18 because H(18) = 18*(2*18-1) = 630 = 2 * 3^2 * 5 * 7 is a 5-almost prime.

a(20) = 100 because H(100) = 100*(2*100-1) = 19900 = 2^2 * 5^2 * 199 is a 5-almost 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

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Last modified February 25 12:28 EST 2021. Contains 341606 sequences. (Running on oeis4.)