A355382 - OEIS

%I #10 Jul 03 2022 23:56:23

%S 1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,2,1,2,1,1,1,2,1,1,1,2,1,1,1,1,1,1,

%T 1,3,1,1,1,2,1,1,1,2,2,1,1,2,1,2,1,2,1,2,1,2,1,1,1,3,1,1,2,1,1,1,1,2,

%U 1,1,1,3,1,1,2,2,1,1,1,2,1,1,1,3,1,1,1

%N Number of divisors d of n such that bigomega(d) = omega(n).

%C The statistic omega = A001221 counts distinct prime factors (without multiplicity).

%C The statistic bigomega = A001222 counts prime factors with multiplicity.

%C If positive integers are regarded as arrows from the number of prime factors to the number of distinct prime factors, this sequence counts divisible composable pairs. Is there a nice choice of a composition operation making this into an associative category?

%e The set of divisors of 180 satisfying the condition is {12, 18, 20, 30, 45}, so a(180) = 5.

%t Table[Length[Select[Divisors[n],PrimeOmega[#]==PrimeNu[n]&]],{n,100}]

%Y The version with multiplicity is A181591.

%Y For partitions we have A355383, with multiplicity A339006.

%Y The version for compositions is A355384.

%Y Positions of first appearances are A355386.

%Y A000005 counts divisors.

%Y A001221 counts prime indices without multiplicity.

%Y A001222 count prime indices with multiplicity.

%Y A070175 gives representatives for bigomega and omega, triangle A303555.

%Y Cf. A000712, A022811, A056239, A071625, A118914, A133494, A181819, A182850, A323014, A323022, A323023, A355385, A355388.

%K nonn

%O 1,12

%A _Gus Wiseman_, Jul 02 2022