A114556 Numbers n such that n-th heptagonal number is 5-almost prime.

7, 16, 23, 30, 32, 36, 42, 45, 54, 69, 78, 79, 80, 84, 88, 90, 93, 95, 100, 102, 104, 112, 115, 117, 140, 143, 151, 153, 165, 170, 174, 176, 184, 186, 191, 200, 203, 210, 213, 228, 232, 234, 245, 250, 259, 271, 273, 282, 287, 296, 306, 308, 310, 311, 318, 319

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 5-almost prime. n such that A000566(n) is an element of A014614. n such that A001222(A000566(n)) = 5. n such that A001222(n*(5*n-3)/2) = 5.

Example

a(1) = 7 because Hep(7) = 7*(5*7-3)/2 = 112 = 2^4 * 7 is 5-almost prime [also 112 = Hep(7) = Hep(Hep(2)) is an iterated heptagonal number].
a(2) = 16 because Hep(16) = 16*(5*16-3)/2 = 616 = 2^3 * 7 * 11 is 5-almost prime.
a(3) = 23 because Hep(23) = 23*(5*23-3)/2 = 1288 = 2^3 * 7 * 23.
a(18) = 100 because Hep(100) = 100*(5*100-3)/2 = 24850 = 2 * 5^2 * 7 * 71.
a(21) = 112 because Hep(112) = 112*(5*112-3)/2 = 31192 = 2^3 * 7 * 557 [also 31192 = Hep(112) = Hep(Hep(7)) = Hep(Hep(Hep(2))) is an iterated heptagonal number].

Mathematica

Select[Range[400], PrimeOmega[# (5 # - 3)/2] == 5 &] (* Giovanni Resta, Jun 14 2016 *)
Select[Range[400], PrimeOmega[PolygonalNumber[7, #]]==5&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Sep 22 2020 *)

Crossrefs

Cf. A000040, A000566, A001222, A001358, A014614.

Sequence in context: A342743 A368407 A044440 * A136772 A190371 A367084

Adjacent sequences: A114553 A114554 A114555 * A114557 A114558 A114559

Keyword

easy,nonn

Author

Jonathan Vos Post, Feb 15 2006

Extensions

Corrected and extended by Giovanni Resta, Jun 14 2016

Status

approved