

A113619


Heptagonfree numbers.


1



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
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OFFSET

1,2


COMMENTS

Heptagonal number analogy of A112886 (the trianglefree 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*n3)/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(5n3))/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: A023801 A267305 A302478 * A004765 A247063 A003726
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



