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%I #16 Dec 24 2018 13:09:39
%S 1,2,7,11,13,14,17,19,23,26,29,31,34,37,38,41,43,46,47,53,58,59,61,62,
%T 67,71,73,74,77,79,82,83,86,89,94,97,101,103,106,107,109,113,118,119,
%U 122,127,131,133,134,137,139,142,143,146,149,151,157,158,161,163
%N Numbers simultaneously pentagon-free, squarefree and triangle-free.
%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. "The Number of Squarefree Numbers." 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 and Charles R Greathouse IV, <a href="/A113544/b113544.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from Greubel)
%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 a*(a+1)/2 nor b^2 nor c*(3*c-1)/2. A005117 INTERSECTION A112886 INTERSECTION A113508.
%t bad = Rest@ Union[# (# + 1)/2 &@ Range[19], Range[14]^2, # (3 # - 1)/2 &@ Range[11]]; Select[Range[200], {} == Intersection[bad, Divisors[#]] &] (* _Giovanni Resta_, Jun 13 2016 *)
%o (PARI) list(lim)=my(v=List()); forsquarefree(n=1,lim\1, fordiv(n,d, if((ispolygonal(d,3) || ispolygonal(d,5)) && d>1, next(2))); listput(v,n[1])); Vec(v); \\ _Charles R Greathouse IV_, Dec 24 2018
%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 Corrected and extended by _Giovanni Resta_, Jun 13 2016
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