A378181 - OEIS

%I #5 Nov 24 2024 09:38:54

%S 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,

%T 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,

%U 3,10,1,6,3,10,1,15,1,3,6,6,3,10,1,15,4,3,1

%N a(1) = 0, a(n) = binomial(bigomega(n) + omega(n) - 1, omega(n)), where bigomega = A001222 and omega = A001221.

%H Michael De Vlieger, <a href="/A378181/b378181.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = cardinality of { m : rad(m) | n, bigomega(m) < bigomega(n) }, i.e., row n of A378180.

%F For prime p, a(p) = A010846(p)-1 = A000005(p)-1 = 1.

%F For prime power p^k, a(p^k) = A010846(p^k)-1 = A000005(p^k)-1 = k.

%F For n in A024619, a(n) != A010846(n).

%t {0}~Join~Table[Binomial[PrimeOmega[n] + # - 1, #] &@ PrimeNu[n], {n, 120}]

%Y Cf. A000005, A001221, A001222, A007947, A010846, A024619, A378180.

%K nonn,easy

%O 1,4

%A _Michael De Vlieger_, Nov 19 2024