A383213 - OEIS

A383213

a(n) = number of distinct prime factors of binomial(2n,n+1).

0, 1, 2, 2, 4, 3, 4, 4, 5, 5, 6, 6, 6, 7, 6, 7, 9, 8, 10, 9, 10, 10, 10, 9, 10, 10, 11, 11, 12, 13, 12, 12, 14, 14, 14, 14, 14, 14, 16, 14, 16, 15, 16, 17, 16, 17, 18, 17, 18, 18, 18, 18, 20, 18, 20, 19, 19, 20, 20, 21, 21, 21, 21, 21, 23, 22, 24, 23, 23, 23

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OFFSET

1,3

LINKS

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

EXAMPLE

binomial(6,4)= 3*5, so a(3)=2.

MATHEMATICA

Table[PrimeNu[Binomial[2 n, n + 1]], {n, 200}]

PROG

(PARI) a(n) = omega(binomial(2*n, n+1)); \\ Michel Marcus, Apr 19 2025

(Python)

from collections import Counter

from sympy import factorint

def A383213(n): return len(sum((Counter(factorint(i)) for i in range(n+2, (n<<1)+1)), start=Counter())-sum((Counter(factorint(i)) for i in range(1, n)), start=Counter())) # Chai Wah Wu, Apr 26 2025

CROSSREFS

Cf. A000984, A001221, A067434, A383214.

Sequence in context: A087808 A217754 A319397 * A094950 A087874 A363341

Adjacent sequences: A383210 A383211 A383212 * A383214 A383215 A383216

KEYWORD

nonn

AUTHOR

Clark Kimberling, Apr 19 2025

STATUS

approved