A114548 Numbers n such that n-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

1,1

Comments

Hep(2) = 7 is the only prime heptagonal number.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Heptagonal Number.

Eric Weisstein's World of Mathematics, Almost Prime.

Formula

n such that Hep(n) = n*(5*n-3)/2 is 3-almost prime. n such that A000566(n) is an element of A014612. n such that A001222(A000566(n)) = 3. n such that A001222(n*(5*n-3)/2) = 3.

Example

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).

Mathematica

Select[Range[400], PrimeOmega[# (5 # - 3)/2] == 3 &] (* Giovanni Resta, Jun 14 2016 *)
Select[Range[250], PrimeOmega[PolygonalNumber[7, #]]==3&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Sep 04 2020 *)

Crossrefs

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

Sequence in context: A294478 A154485 A105410 * A182759 A022121 A364086

Adjacent sequences: A114545 A114546 A114547 * A114549 A114550 A114551

Keyword

easy,nonn

Author

Jonathan Vos Post, Feb 15 2006

Extensions

Corrected and extended by Giovanni Resta, Jun 14 2016

Status

approved