|
%I #9 May 02 2019 18:58:57
%S 60,63,72,114,144,159,167,180,183,207,216,225,247,255,275,297,312,315,
%T 320,330,343,352,360,378,387,391,399,405,408,411,416,420,429,440,447,
%U 448,450,459,465,468,483,486,504,513,520,525,531,546,588,591,594,609
%N Numbers n such that n-th heptagonal number is 7-almost prime.
%C Hep(2) = 7 is the only prime heptagonal number.
%H Harvey P. Dale, <a href="/A114559/b114559.txt">Table of n, a(n) for n = 1..2000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HeptagonalNumber.html">Heptagonal Number.</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/AlmostPrime.html">Almost Prime.</a>
%F n such that Hep(n) = n*(5*n-3)/2 is 7-almost prime. n such that A000566(n) is an element of A046308. n such that A001222(A000566(n)) = 7. n such that A001222(n*(5*n-3)/2) = 7.
%e a(1) = 60 because Hep(60) = 60*(5*60-3)/2 = 8910 = 2 * 3^4 * 5 * 11 is 7-almost prime.
%e a(2) = 63 because Hep(63) = 63*(5*63-3)/2 = 9828 = 2^2 * 3^3 * 7 * 13 is 7-almost prime.
%e a(3) = 72 because Hep(72) = 72*(5*72-3)/2 = 12852 = 2^2 * 3^3 * 7 * 17 is 7-almost prime.
%e a(4) = 114 because Hep(114) = 114*(5*114-3)/2 = 32319 = 3^5 * 7 * 19 is 7-almost prime.
%t Select[Range[250],PrimeOmega[(#(5#-3))/2]==7&] (* _Harvey P. Dale_, May 02 2019 *)
%Y Cf. A000040, A000566, A001222, A001358, A046308.
%K easy,nonn
%O 1,1
%A _Jonathan Vos Post_, Feb 15 2006
%E More terms from _Harvey P. Dale_, May 02 2019
|
