%I #11 May 06 2017 23:41:58

%S 1,2,3,6,7,11,13,14,17,19,21,23,26,29,31,33,34,37,38,39,41,42,43,46,

%T 47,53,57,58,59,61,62,67,69,71,73,74,77,78,79,82,83,86,87,89,91,93,94,

%U 97,101,103,106,107,109,111,113,114,118,119,122,123,127,129

%N Numbers both pentagon-free and squarefree.

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

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

%D 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.

%H G. C. Greubel, <a href="/A113545/b113545.txt">Table of n, a(n) for n = 1..1000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Squarefree.html">Squarefree.</a>

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

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

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

%K easy,nonn

%O 1,2

%A _Jonathan Vos Post_, Jan 13 2006

%E Data corrected by _Giovanni Resta_, Jun 13 2016