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A378181
a(1) = 0, a(n) = binomial(bigomega(n) + omega(n) - 1, omega(n)), where bigomega = A001222 and omega = A001221.
3
0, 1, 1, 2, 1, 3, 1, 3, 2, 3, 1, 6, 1, 3, 3, 4, 1, 6, 1, 6, 3, 3, 1, 10, 2, 3, 3, 6, 1, 10, 1, 5, 3, 3, 3, 10, 1, 3, 3, 10, 1, 10, 1, 6, 6, 3, 1, 15, 2, 6, 3, 6, 1, 10, 3, 10, 3, 3, 1, 20, 1, 3, 6, 6, 3, 10, 1, 6, 3, 10, 1, 15, 1, 3, 6, 6, 3, 10, 1, 15, 4, 3, 1
OFFSET
1,4
LINKS
FORMULA
a(n) = cardinality of { m : rad(m) | n, bigomega(m) < bigomega(n) }, i.e., row n of A378180.
For prime p, a(p) = A010846(p)-1 = A000005(p)-1 = 1.
For prime power p^k, a(p^k) = A010846(p^k)-1 = A000005(p^k)-1 = k.
For n in A024619, a(n) != A010846(n).
MATHEMATICA
{0}~Join~Table[Binomial[PrimeOmega[n] + # - 1, #] &@ PrimeNu[n], {n, 120}]
KEYWORD
nonn,easy
AUTHOR
Michael De Vlieger, Nov 19 2024
STATUS
approved