A114548 Numbers k such that k-th heptagonal number is 3-almost prime.

3, 8, 11, 19, 20, 25, 28, 37, 38, 43, 52, 58, 59, 67, 68, 70, 77, 82, 83, 85, 86, 89, 92, 98, 106, 110, 116, 124, 130, 131, 133, 134, 137, 139, 142, 149, 157, 161, 169, 172, 179, 181, 182, 185, 188, 190, 193, 202, 206, 209, 211, 214, 217, 227, 233, 238, 244

Offset: 1

Author

Jonathan Vos Post, Feb 15 2006

Keywords

• easy
• nonn

Examples

			a(1) = 3 because Hep(3) = 3*(5*3-3)/2 = 18 = 2 * 3^2 is 3-almost prime.
a(2) = 8 because Hep(8) = 8*(5*8-3)/2 = 148 = 2^2 * 37 is 3-almost prime.
a(3) = 11 because Hep(11) = 11*(5*11-3)/2 = 286 = 2 * 11 * 13 is 3-almost prime.
a(17) = 82 because Hep(82) = 82*(5*82-3)/2 = 16687 = 11 * 37 * 41 is 3-almost prime (and 3-brilliant).
		

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, Heptagonal Number.

Crossrefs

Cf. A000040, A000566, A001222, A001358, A014612, A099153.

Programs

Mathematica

Select[Range[400], PrimeOmega[# (5 # - 3)/2] == 3 &] (* Giovanni Resta, Jun 14 2016 *)
Select[Range[250],PrimeOmega[PolygonalNumber[7,#]]==3&] (* Harvey P. Dale, Sep 04 2020 *)

Formula

Numbers k such that Hep(k) = k*(5*k-3)/2 is 3-almost prime.

Numbers k such that A000566(k) is a term of A014612.

Numbers k such that A001222(A000566(k)) = 3.

Numbers k such that A001222(k*(5*k-3)/2) = 3.

Extensions

Corrected and extended by Giovanni Resta, Jun 14 2016