A255133 Number of unitary divisors of odd Catalan numbers (A038003).

1, 1, 2, 8, 64, 2048, 1048576, 68719476736, 18446744073709551616, 166153499473114484112975882535043072, 822752278660603021077484591278675252491367932816789931674304512, 4925250774549309901534880012517951725634967408808180833493536675530715221437151326426783281860614455100828498788352

Offset

0,3

Links

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

Formula

a(n) = A034444(A038003(n)).

Example

A038003(4) = 9694845 which has 64 unitary divisors.

Prog

(Python)
from operator import mul
from functools import reduce
from sympy import factorint
A255133_list, c, s = [1, 1], {}, 3
for n in range(2, 2**17):
....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 = 2**len(c)
........A255133_list.append(c2)
........s = 2*s+1

Crossrefs

Cf. A038003, A034444, A119861, A119908, A120274, A120275, A255132.

Sequence in context: A006119 A296328 A322066 * A073113 A361007 A091794

Adjacent sequences: A255130 A255131 A255132 * A255134 A255135 A255136

Keyword

nonn

Author

Chai Wah Wu, Feb 15 2015

Status

approved