A113508 Pentagon-free numbers: numbers k such that no divisor of k is a pentagonal number > 1.

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, 37, 38, 39, 41, 42, 43, 46, 47, 49, 52, 53, 54, 56, 57, 58, 59, 61, 62, 63, 64, 67, 68, 69, 71, 73, 74, 76, 77, 78, 79, 81, 82, 83, 86, 87, 89, 91, 93, 94, 97, 98, 99, 101

Offset: 1

Author

Jonathan Vos Post, Jan 11 2006

Keywords

• easy
• nonn

Comments

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

Density is empirically close to 12/(Pi^(5/2)). - Richard Peterson, Apr 06 2025

Examples

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

Links

• G. C. Greubel, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A000326, A112886, A113502.

Programs

Mathematica

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

PARI

is(n)=fordiv(n, d, if(ispolygonal(d, 5) && d>1, return(0))); 1 \\ Charles R Greathouse IV, Dec 24 2018

Extensions

Data corrected by Giovanni Resta, Jun 13 2016

a(1)=1 inserted by Andrew Howroyd, Sep 08 2024