A268083 Numbers n that are not prime powers and such that gcd(binomial(2*n-1,n), n) = 1.

39, 55, 93, 111, 119, 155, 161, 185, 253, 275, 279, 305, 327, 333, 351, 363, 377, 403, 407, 413, 497, 511, 517, 533, 559, 629, 635, 649, 655, 685, 689, 697, 707, 741, 749, 755, 779, 785, 791, 813, 817, 849, 871, 893, 901, 905, 923, 981, 1003, 1011, 1027, 1043

Offset

1,1

Comments

It seems there is a typo in the Gua and Zeng link, it gives 175 instead of 185 as a term.

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Victor J.W. Guo and Jiang Zeng, Factors of binomial sums from the Catalan triangle, Journal of Number Theory 130 (2010) 172-186.

Mathematica

Select[Range[2, 1100], !PrimePowerQ[#]&&GCD[Binomial[2#-1, #], #]==1&] (* Harvey P. Dale, May 26 2020 *)

Prog

(PARI) isok(n) = (n != 1) && !isprimepower(n) && (gcd(binomial(2*n-1, n), n) == 1);
(Magma) [n : n in [2..2000] | not IsPrimePower(n) and Gcd(Binomial(2*n-1, n), n) eq 1]; // Vincenzo Librandi, Jan 26 2016
(Python)
from __future__ import division
from fractions import gcd
from sympy import factorint
A268083_list, b = [], 1
for n in range(1, 10**4):
    if len(factorint(n)) > 1 and gcd(b, n) == 1:
        A268083_list.append(n)
    b = b*2*(2*n+1)//(n+1) # Chai Wah Wu, Jan 26 2016

Crossrefs

Cf. A000961, A088218, A268082.

Sequence in context: A227735 A319983 A165346 * A063480 A305026 A009633

Adjacent sequences: A268080 A268081 A268082 * A268084 A268085 A268086

Keyword

nonn

Author

Michel Marcus, Jan 26 2016

Status

approved