A177202 Nontrivially polygonal-free numbers.

1, 2, 3, 4, 5, 7, 8, 11, 13, 14, 17, 19, 23, 26, 29, 31, 37, 38, 41, 43, 47, 53, 59, 61, 62, 67, 71, 73, 74, 77, 79, 83, 86, 89, 97, 101, 103, 107, 109, 113, 119, 122, 127, 131, 134, 137, 139, 143, 146, 149, 151, 157, 158, 161, 163, 167, 173, 179

Offset: 1

Author

Jonathan Vos Post, May 04 2010

Keywords

• easy
• nonn

Comments

Positive integers which are not multiples of any nontrivially polygonal numbers A090466. Generalization of squarefree numbers: numbers that are not divisible by a square greater than 1 (A005117) where "square" is replaced by triangular, square, pentagonal, hexagonal, and so forth. Positive integers which are not positive integer multiples of numbers in the array of A057145 below the second row (which has every positive integer) and right of the 2nd column (which has every positive integer). That is, positive integers which are not positive integer multiples of any triangular number >3, any square >4, any pentagonal number >5, any hexagonal number >6, any heptagonal number >7, any octagonal number >8, any 9-gonal (nonagonal) number >9 and so forth. Properly includes all primes.

Crossrefs

Cf. A090466, A177201.

Formula

Complement of A177201.

Extensions

Corrected and extended by Sean A. Irvine, Apr 09 2013