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

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, 784, 786, 5, 8, 15, 16, 17, 20, 35, 42, 45, 50, 51, 52, 53, 56, 59, 60, 77, 80, 133, 134, 135, 136, 156, 157, 158, 159, 160, 161, 170, 210, 211, 212, 400, 401, 402, 651, 652, 785

Offset

0,3

Comments

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.

Links

T. D. Noe, Rows n = 0..40 of irregular triangle, flattened

Example

The irregular triangle begins:
0, 1, 2, 4
3, 6, 7, 9,..., 784, 786
5, 8, 15, 16,..., 652, 785
13, 14, 18, 19,..., 445, 2080
25, 26, 27, 32,..., 783, 902
61, 62, 63, 64,..., 2033, 2034

Mathematica

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]]]}]

Crossrefs

Cf. A059097 (union of first two rows), A110493, A110494, A239623, A239624.

Sequence in context: A006016 A227413 A217122 * A245604 A054239 A305424

Adjacent sequences: A239619 A239620 A239621 * A239623 A239624 A239625

Keyword

nonn,tabf

Author

T. D. Noe, Mar 27 2014

Status

approved