A255133 Number of unitary divisors of odd Catalan numbers (A038003).
1, 1, 2, 8, 64, 2048, 1048576, 68719476736, 18446744073709551616, 166153499473114484112975882535043072, 822752278660603021077484591278675252491367932816789931674304512, 4925250774549309901534880012517951725634967408808180833493536675530715221437151326426783281860614455100828498788352
Offset: 0
Keywords
Examples
A038003(4) = 9694845 which has 64 unitary divisors.
Links
- Chai Wah Wu, Table of n, a(n) for n = 0..14
Programs
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Mathematica
a[n_] := 2^PrimeNu[CatalanNumber[2^n-1]]; Array[a, 12, 0] (* Amiram Eldar, Oct 04 2024 *)
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PARI
a(n) = 1 << omega(binomial(2^(n+1)-2, 2^n-1)/(2^n)); \\ Amiram Eldar, Oct 04 2024
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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**16): 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