A113545 Numbers both pentagon-free and squarefree.

1, 2, 3, 6, 7, 11, 13, 14, 17, 19, 21, 23, 26, 29, 31, 33, 34, 37, 38, 39, 41, 42, 43, 46, 47, 53, 57, 58, 59, 61, 62, 67, 69, 71, 73, 74, 77, 78, 79, 82, 83, 86, 87, 89, 91, 93, 94, 97, 101, 103, 106, 107, 109, 111, 113, 114, 118, 119, 122, 123, 127, 129

Offset

1,2

References

Bellman, R. and Shapiro, H. N. "The Distribution of Squarefree Integers in Small Intervals." Duke Math. J. 21, 629-637, 1954.

Borwein, J. and Bailey, D. Mathematics by Experiment: Plausible Reasoning in the 21st Century. Natick, MA: A. K. Peters, 2003.

Hardy, G. H. and Wright, E. M., Section 18.6 in An Introduction to the Theory of Numbers, 5th ed. Oxford, England: Clarendon Press, pp. 269-270, 1979.

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Squarefree.

Formula

a(n) has no factor >1 of form b^2 nor c*(3*c-1)/2. A005117 INTERSECTION A113508.

Mathematica

bad = Rest@Union[Range[14]^2, # (3 # - 1)/2 &@ Range[11]]; Select[ Range[200], {} == Intersection[ bad, Divisors[#]] &] (* Giovanni Resta, Jun 13 2016 *)

Crossrefs

Cf. A000217, A005117, A113502, A013929, A046098, A059956, A065474, A071172, A087618, A088454, A112886, A113508.

Sequence in context: A350573 A274546 A366641 * A056825 A372062 A070757

Adjacent sequences: A113542 A113543 A113544 * A113546 A113547 A113548

Keyword

easy,nonn

Author

Jonathan Vos Post, Jan 13 2006

Extensions

Data corrected by Giovanni Resta, Jun 13 2016

Status

approved