A113619 - OEIS

%I #25 Sep 09 2024 09:36:14

%S 1,2,3,4,5,6,8,9,10,11,12,13,15,16,17,19,20,22,23,24,25,26,27,29,30,

%T 31,32,33,37,38,39,40,41,43,44,45,46,47,48,50,51,52,53,57,58,59,60,61,

%U 62,64,65,66,67,69,71,73,74,75,76,78,79,80,82,83,85,86,87,88,89,92,93,94,95,96,97,99,100

%N Heptagon-free numbers: numbers k such that no divisor of k is a heptagonal number > 1.

%C Heptagonal number analogy of A112886 (the triangle-free positive integers).

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HeptagonalNumber.html">Heptagonal Number.</a>

%e 7 is the first nontrivial heptagonal number, so no multiple of 7 is a term.

%t upto=100;Module[{maxhep=Floor[(3+Sqrt[9+40upto])/10],heps}, heps= Rest[ Table[(n(5n-3))/2,{n,maxhep}]];Complement[Range[upto],Union[ Flatten[ Table[n*heps,{n,Ceiling[upto/7]}]]]]] (* _Harvey P. Dale_, May 19 2012 *)

%Y Cf. A000566, A112886, A113502.

%K easy,nonn

%O 1,2

%A _Jonathan Vos Post_, Jan 14 2006

%E Corrected by _Harvey P. Dale_, May 19 2012