This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A056651 #18 Jul 22 2024 15:23:07
%S A056651 0,1,2,3,4,5,6,7,8,9,10,11,12,13,15,16,17,18,19,20,21,23,24,25,31,32,
%T A056651 35,36,37,39,40,41,43,47,48,49,55,63,64,65,66,67,68,69,71,72,73,75,79,
%U A056651 80,95,96,97,111,129,130,131,132,133,143,144,151,161,163,167,191,192,193
%N A056651 Numbers k such that binomial(k,floor(k/2)) has no non-unitary square divisors: all of their square divisors are unitary ones.
%C A056651 This property is weaker than "squarefreedom", but shows how central binomial coefficients are "poor of squares".
%C A056651 Numbers k such that binomial(k,floor(k/2)) is cubefree (A004709). - _Amiram Eldar_, Jul 22 2024
%H A056651 T. D. Noe, <a href="/A056651/b056651.txt">Table of n, a(n) for n = 1..129</a> (no others < 10^8)
%e A056651 223 is a term because 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.
%t A056651 Select[Range[0, 11000], AllTrue[FactorInteger[Binomial[#, Floor[#/2]]][[;;, 2]], #1 <= 2 &] &] (* _Amiram Eldar_, Jul 22 2024 *)
%o A056651 (PARI) is(n) = if(n <= 1, 1, vecmax(factor(binomial(n, floor(n/2)))[, 2]) < 3); \\ _Amiram Eldar_, Jul 22 2024
%Y A056651 Cf. A001405, A004709, A046098, A056175, A110495.
%K A056651 nonn
%O A056651 1,3
%A A056651 _Labos Elemer_, Aug 09 2000