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%I A113545 #11 May 06 2017 23:41:58
%S A113545 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 A113545 47,53,57,58,59,61,62,67,69,71,73,74,77,78,79,82,83,86,87,89,91,93,94,
%U A113545 97,101,103,106,107,109,111,113,114,118,119,122,123,127,129
%N A113545 Numbers both pentagon-free and squarefree.
%D A113545 Bellman, R. and Shapiro, H. N. "The Distribution of Squarefree Integers in Small Intervals." Duke Math. J. 21, 629-637, 1954.
%D A113545 Borwein, J. and Bailey, D. Mathematics by Experiment: Plausible Reasoning in the 21st Century. Natick, MA: A. K. Peters, 2003.
%D A113545 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 A113545 G. C. Greubel, <a href="/A113545/b113545.txt">Table of n, a(n) for n = 1..1000</a>
%H A113545 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Squarefree.html">Squarefree.</a>
%F A113545 a(n) has no factor >1 of form b^2 nor c*(3*c-1)/2. A005117 INTERSECTION A113508.
%t A113545 bad = Rest@Union[Range[14]^2, # (3 # - 1)/2 &@ Range[11]]; Select[ Range[200], {} == Intersection[ bad, Divisors[#]] &] (* _Giovanni Resta_, Jun 13 2016 *)
%Y A113545 Cf. A000217, A005117, A113502, A013929, A046098, A059956, A065474, A071172, A087618, A088454, A112886, A113508.
%K A113545 easy,nonn
%O A113545 1,2
%A A113545 _Jonathan Vos Post_, Jan 13 2006
%E A113545 Data corrected by _Giovanni Resta_, Jun 13 2016

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