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A376567
a(n) = binomial(bigomega(n) + omega(n), omega(n)), where bigomega = A001222 and omega = A001221.
3
1, 2, 2, 3, 2, 6, 2, 4, 3, 6, 2, 10, 2, 6, 6, 5, 2, 10, 2, 10, 6, 6, 2, 15, 3, 6, 4, 10, 2, 20, 2, 6, 6, 6, 6, 15, 2, 6, 6, 15, 2, 20, 2, 10, 10, 6, 2, 21, 3, 10, 6, 10, 2, 15, 6, 15, 6, 6, 2, 35, 2, 6, 10, 7, 6, 20, 2, 10, 6, 20, 2, 21, 2, 6, 10, 10, 6, 20, 2
OFFSET
1,2
COMMENTS
For prime power p^k, a(p^k) = A010846(p^k) = A000005(p^k) = k+1. Therefore, for prime p, a(p) = A010846(p) = A000005(p) = 2.
For n in A024619, a(n) != A010846(n) and A010846(n) > A000005(n).
LINKS
FORMULA
a(n) = length of row n of A376248.
a(n) = A010846(n) - A376846(n) + A376847(n).
MAPLE
with(NumberTheory):
a := n -> binomial(Omega(n) + Omega(n, distinct), Omega(n, distinct)):
seq(a(n), n = 1..79); # Peter Luschny, Oct 25 2024
MATHEMATICA
Array[Binomial[#2 + #1, #1] & @@ {PrimeNu[#], PrimeOmega[#]} &, 120]
KEYWORD
nonn,easy,changed
AUTHOR
Michael De Vlieger, Oct 09 2024
STATUS
approved