A290584 a(n) is the factor P(n) having prime factors between n^2 and 2*n^2 in A285388(n) = R(n)P(n) for n > 1, a(1)=1.

1, 35, 2431, 6678671, 2756205443, 2781907990776503, 3749562977351496827, 34227405074603836560875299, 10994118229823875586790445536799, 3383080509296917481189798760796480670771162183

Offset

1,2

Comments

All A290564(n) prime factors in the interval occur with multiplicity 1. Thus a(n) is squarefree.

Links

Table of n, a(n) for n=1..10.

Formula

a(n) = A285388(n)/A290583(n).

Example

a(3) = 2431: A285388(3) = 36465 = (R(3) = 15)*(P(3) = 11*13*17 = 2431);
a(4) = 6678671: A285388(4) = 300540195 = (R(4) = 45)*(P(4) = 17*19*23*29*31 = 6678671).

Mathematica

Table[First@ Apply[Times, Map[Power, #]] &@ Select[FactorInteger@ Numerator[Sum[Binomial[2 k, k]/4^k, {k, 0, n^2 - 1}]/n], Function[p, # <= First@ p < 2 #] &[n^2]], {n, 10}] (* Michael De Vlieger, Aug 10 2017 *)

Prog

(PARI) a285388(n) = my(m=n*binomial(2*n^2, n^2)); m>>valuation(m, 2);
a(n) = if (n==1, 1, my(f=factor(a285388(n))); for (k=1, #f~, if ((n^2 > f[k, 1]) || (f[k, 1] > 2*n^2), f[k, 1] = 1)); factorback(f)); \\ Michel Marcus, Aug 07 2017

Crossrefs

Cf. A285388, A290583 (R()), A290564 (number of primes in interval).

Sequence in context: A202921 A215291 A249886 * A174749 A184124 A343586

Adjacent sequences: A290581 A290582 A290583 * A290585 A290586 A290587

Keyword

nonn

Author

Ralf Steiner, Aug 07 2017

Status

approved