%I #21 Sep 08 2024 22:43:56

%S 1,2,3,4,6,7,8,9,11,13,14,16,17,18,19,21,23,26,27,28,29,31,32,33,34,

%T 37,38,39,41,42,43,46,47,49,52,53,54,56,57,58,59,61,62,63,64,67,68,69,

%U 71,73,74,76,77,78,79,81,82,83,86,87,89,91,93,94,97,98,99,101

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

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

%H G. C. Greubel, <a href="/A113508/b113508.txt">Table of n, a(n) for n = 1..5000</a>

%e 10 is not a term, since 10 = 2 * 5 and 5 is the first nontrivial pentagonal number.

%e 24 is not a term, since 12|24 and 12 is a pentagonal number.

%e 44 is not a term, since 22|44 and 22 is a pentagonal number.

%t Select[Range[1, 101], {} == Intersection[{5, 12, 22, 35, 51, 70, 92}, Divisors[#]] &] (* _Giovanni Resta_, Jun 13 2016 *)

%o (PARI) is(n)=fordiv(n, d, if(ispolygonal(d, 5) && d>1, return(0))); 1 \\ _Charles R Greathouse IV_, Dec 24 2018

%Y Cf. A000326, A112886, A113502.

%K easy,nonn

%O 1,2

%A _Jonathan Vos Post_, Jan 11 2006

%E Data corrected by _Giovanni Resta_, Jun 13 2016

%E a(1)=1 inserted by _Andrew Howroyd_, Sep 08 2024