A255132 Number of divisors of odd Catalan numbers (A038003).

1, 1, 2, 8, 96, 2048, 3145728, 206158430208, 27670116110564327424, 498460498419343452338927647605129216, 24991100464315816765228594460089760794425300959309994174606999552, 336610107623104398583024455855523763248864803845734108839073897168302318415095310965480469919661369165797247714066432

Offset: 0

Author

Chai Wah Wu, Feb 15 2015

Keywords

• nonn

Examples

			A038003(4) = 9694845 which has 96 divisors.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 0..14

Crossrefs

Cf. A038003, A000005, A119861, A119908, A120274, A120275, A255133.

Programs

Python

from operator import mul
from functools import reduce
from sympy import factorint
A255132_list, c, s = [1, 1], {}, 3
for n in range(2,2**15):
    for p,e in factorint(4*n-2).items():
        if p in c:
            c[p] += e
        else:
            c[p] = e
    for p,e in factorint(n+1).items():
        if c[p] == e:
            del c[p]
        else:
            c[p] -= e
    if n == s:
        c2 = reduce(mul,[e+1 for e in c.values()])
        A255132_list.append(c2)
        s = 2*s+1

Formula

a(n) = A000005(A038003(n)).