A396020 Sum of the distinct prime divisors of C(9*n, n).

3, 20, 21, 43, 105, 98, 202, 210, 242, 316, 331, 506, 507, 412, 541, 721, 890, 818, 855, 1088, 1001, 1410, 1367, 1540, 1341, 1831, 2009, 2008, 1887, 2091, 2555, 2809, 2635, 2427, 3037, 2911, 3102, 3348, 3478, 3655, 3927, 3785, 4499, 4518, 4600, 4684, 5385, 5054

Offset

1,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Formula

a(n) = sopf(binomial(9*n,n)) = A008472(A169958(n)).

Example

a(2) = 20 because binomial(18,2) = 153 = 3^2*17 and 3+17 = 20.
a(3) = 21 because binomial(27,3) = 2925 = 3^2*5^2*13 and 3+5+13 = 21.

Maple

f:= n -> convert(NumberTheory:-PrimeFactors(binomial(9*n, n)), `+`):
map(f, [$1..100]); # Robert Israel, May 17 2026

Mathematica

a[n_]:=Total[FactorInteger[Binomial[9*n, n]][[All, 1]]]; Table[a[n], {n, 1, 48}]

Prog

(Magma) a := func<n | &+PrimeDivisors(Binomial(9*n, n))>; N := 48; [a(n) : n in [1..N]];
(Python)
from collections import Counter
from sympy import factorint
def A396020(n):
    c = Counter()
    for i in range(8*n+1, 9*n+1):
        c += factorint(i)
    for i in range(2, n+1):
        c -= factorint(i)
    return sum(c) # Chai Wah Wu, May 17 2026

Crossrefs

Cf. A008472, A034387, A169958, A394454, A394591, A394592, A394593, A395515, A395566, A395603.

Sequence in context: A212995 A081849 A333667 * A375618 A169642 A222482

Adjacent sequences: A396017 A396018 A396019 * A396021 A396022 A396023

Keyword

nonn

Author

Vincenzo Librandi, May 17 2026

Status

approved