A113619 Heptagon-free numbers.

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

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..77.

J. V. Post, Table of Polytope Numbers, Sorted, Through 1,000,000.

Eric Weisstein's World of Mathematics, Heptagonal Number.

Formula

{a(n)} = {integers k>1: no divisor of k is a heptagonal number n*(5*n-3)/2}>1}.

{a(n)} = {integers k>1: no divisor of k is in A000566 and >1}.

Example

7 = Hep(2) is the first nontrivial heptagonal number, so neither 7 nor any multiple of 7 is in this sequence. 18 = Hep(3) is the first nontrivial heptagonal number, so neither 18 nor any multiple of 18 is in this sequence. 34 = Hep(4) is the first nontrivial heptagonal number, so neither 34 nor any multiple of 34 is in this sequence. Similarly for Hep(5) = 55, Hep(6) = 81, Hep(7) = 112. Hence three consecutive integers are excluded with 54 = 3*18, 55 = Hep(5), 56 = 7*8.

Mathematica

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 *)

Crossrefs

Cf. A000566, A112886, A113502.

Sequence in context: A267305 A302478 A356939 * A325114 A004765 A247063

Adjacent sequences: A113616 A113617 A113618 * A113620 A113621 A113622

Keyword

easy,nonn

Author

Jonathan Vos Post, Jan 14 2006

Extensions

Corrected by Harvey P. Dale, May 19 2012

Status

approved