This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A355382 #10 Jul 03 2022 23:56:23
%S A355382 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 A355382 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 A355382 1,1,1,3,1,1,2,2,1,1,1,2,1,1,1,3,1,1,1
%N A355382 Number of divisors d of n such that bigomega(d) = omega(n).
%C A355382 The statistic omega = A001221 counts distinct prime factors (without multiplicity).
%C A355382 The statistic bigomega = A001222 counts prime factors with multiplicity.
%C A355382 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 A355382 The set of divisors of 180 satisfying the condition is {12, 18, 20, 30, 45}, so a(180) = 5.
%t A355382 Table[Length[Select[Divisors[n],PrimeOmega[#]==PrimeNu[n]&]],{n,100}]
%Y A355382 The version with multiplicity is A181591.
%Y A355382 For partitions we have A355383, with multiplicity A339006.
%Y A355382 The version for compositions is A355384.
%Y A355382 Positions of first appearances are A355386.
%Y A355382 A000005 counts divisors.
%Y A355382 A001221 counts prime indices without multiplicity.
%Y A355382 A001222 count prime indices with multiplicity.
%Y A355382 A070175 gives representatives for bigomega and omega, triangle A303555.
%Y A355382 Cf. A000712, A022811, A056239, A071625, A118914, A133494, A181819, A182850, A323014, A323022, A323023, A355385, A355388.
%K A355382 nonn
%O A355382 1,12
%A A355382 _Gus Wiseman_, Jul 02 2022