

A113508


Pentagonfree numbers.


4



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
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OFFSET

1,1


COMMENTS

Pentagonal number analogy of A112886 (the trianglefree positive integers).


LINKS

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


FORMULA

{a(n)} = {integers k>1: no divisor of k is a pentagonal number n*(3*n1)/2}>1}. {a(n)} = {integers k>1: no divisor of k is an element of A000326 > 1}.


EXAMPLE

10 is not an element, since 10 = 2 * 5 and 5 is the first nontrivial pentagonal number. 24 is not an element, since 1224 and 12 is a pentagonal number. 44 is not an element, since 2244 and 22 is a pentagonal number.


MATHEMATICA

Select[Range[2, 101], {} == Intersection[{5, 12, 22, 35, 51, 70, 92}, Divisors[#]] &] (* Giovanni Resta, Jun 13 2016 *)


PROG

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


CROSSREFS

Cf. A000326, A112886, A113502.
Sequence in context: A140467 A103677 A087919 * A059325 A258938 A004763
Adjacent sequences: A113505 A113506 A113507 * A113509 A113510 A113511


KEYWORD

easy,nonn


AUTHOR

Jonathan Vos Post, Jan 11 2006


EXTENSIONS

Data corrected by Giovanni Resta, Jun 13 2016


STATUS

approved



