Search: id:A056651
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%I A056651
%S A056651 1,2,3,4,5,6,7,8,9,10,11,12,13,15,16,17,18,19,20,21,23,24,25,31,32,35,
%T A056651 36,37,39,40,41,43,47,48,49,55,63,64,65,66,67,68,69,71,72,73,75,79,80,
%U A056651 95,96,97,111,129,130,131,132,133,143,144,151,161,163,167,191,192,193
%N A056651 Numbers n such that binomial[n,Floor[n/2]] has no non-unitary square 
               divisors: all of their square divisors are unitary ones.
%C A056651 This property is weaker than "square-freedom", but shows how central 
               binomial coefficients are "poor of squares".
%H A056651 T. D. Noe, <a href="b056651.txt">Table of n, a(n) for n=1..128</a> (no 
               others < 10^8)
%e A056651 n=223, x=binomial[223,111] has 35 prime divisors. 33 arises at power 
               1. Only 2 and 13 has powers 2>1. So square divisors of x are {1,4,
               169,676}={s}. All of them are also unitary divisors since GCD[s,x/
               s]=1 holds for them.
%Y A056651 A046098, A056175.
%Y A056651 Cf. A110495
%Y A056651 Sequence in context: A023807 A023755 A114886 this_sequence A022772 A004440 
               A026495
%Y A056651 Adjacent sequences: A056648 A056649 A056650 this_sequence A056652 A056653 
               A056654
%K A056651 nonn
%O A056651 1,2
%A A056651 Labos E. (labos(AT)ana.sote.hu), Aug 09 2000

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