cp's OEIS Frontend

A239622 Conjecturally, the irregular triangle of numbers k such that prime(n)^2 is the largest squared prime divisor of binomial(2k,k).

%I A239622 #7 Mar 27 2014 19:24:09
%S A239622 0,1,2,4,3,6,7,9,10,11,12,21,22,28,29,30,31,36,37,54,55,57,58,110,171,
%T A239622 784,786,5,8,15,16,17,20,35,42,45,50,51,52,53,56,59,60,77,80,133,134,
%U A239622 135,136,156,157,158,159,160,161,170,210,211,212,400,401,402,651,652,785
%N A239622 Conjecturally, the irregular triangle of numbers k such that prime(n)^2 is the largest squared prime divisor of binomial(2k,k).
%C A239622 Row 0 lists the numbers k such that binomial(2k,k) is squarefree. Sequence A110494 lists the first term of each row; A239623 lists the conjectured last term; A239624 lists the conjectured length of each row.
%H A239622 T. D. Noe, <a href="/A239622/b239622.txt">Rows n = 0..40 of irregular triangle, flattened</a>
%e A239622 The irregular triangle begins:
%e A239622 0, 1, 2, 4
%e A239622 3, 6, 7, 9,..., 784, 786
%e A239622 5, 8, 15, 16,..., 652, 785
%e A239622 13, 14, 18, 19,..., 445, 2080
%e A239622 25, 26, 27, 32,..., 783, 902
%e A239622 61, 62, 63, 64,..., 2033, 2034
%t A239622 b = 1; t = Table[b = b*(4 - 2/n); last = 0; Do[If[Mod[b, p^2] == 0, last = p], {p, Prime[Range[PrimePi[Sqrt[2*n]]]]}]; last, {n, 20000}]; t = Join[{0}, t]; Table[Flatten[Position[t, p]] - 1, {p, Join[{0}, Prime[Range[20]]]}]
%Y A239622 Cf. A059097 (union of first two rows), A110493, A110494, A239623, A239624.
%K A239622 nonn,tabf
%O A239622 0,3
%A A239622 _T. D. Noe_, Mar 27 2014