A114505 Numbers k such that the k-th hexagonal number is a 7-almost prime.

48, 64, 68, 72, 80, 88, 96, 104, 108, 122, 140, 162, 168, 188, 203, 208, 216, 228, 230, 240, 243, 264, 272, 280, 308, 312, 324, 360, 378, 380, 396, 408, 410, 424, 428, 438, 440, 446, 450, 473, 486, 513, 518, 527, 544, 564, 567, 572, 578, 620, 638, 662, 666, 675, 689, 696

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 A046308.

Numbers k such that A001222(A000384(k)) = 7.

Numbers k such that A001222(k*(2*k-1)) = 7.

Example

a(1) = 48 because HexagonalNumber(48) = H(48) = 48*(2*48-1) = 4560 = 2^4 * 3 * 5 * 19 is a 7-almost prime.
a(2) = 64 because H(64) = 64*(2*64-1) = 8128 = 2^6 * 127 is a 7-almost prime.

Mathematica

Select[Range[800], PrimeOmega[#(2#-1)]==7&] (* Harvey P. Dale, Jul 20 2013 *)
Position[PrimeOmega[PolygonalNumber[6, Range[700]]], 7]//Flatten (* Harvey P. Dale, Jan 10 2024 *)

Crossrefs

Cf. A000384, A001222, A046308.

Sequence in context: A335216 A114821 A108098 * A323610 A186400 A205188

Adjacent sequences: A114502 A114503 A114504 * A114506 A114507 A114508

Keyword

easy,nonn

Author

Jonathan Vos Post, Feb 14 2006

Status

approved