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%I #7 Nov 04 2023 13:16:27
%S 1,1,2,1,1,2,1,3,1,1,1,2,1,4,2,1,1,3,1,1,1,2,1,1,2,3,1,5,1,2,4,1,1,1,
%T 1,2,1,6,1,2,3,1,1,1,2,1,1,1,3,2,1,4,1,2,1,1,7,1,1,2,3,1,5,2,1,1,2,1,
%U 1,8,1,3,4,1,1,2,1,1,2,1,3,1,2,1,1,1,1
%N Unreduced denominator of the n-th divisible pair, where pairs are ordered by Heinz number. Lesser prime index of A318990(n).
%C The Heinz number of a partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k). This gives a bijective correspondence between positive integers and integer partitions.
%F A358103(n) = A358104(n)/a(n).
%e The 12th divisible pair is (2,6) so a(12) = 2.
%t primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t Join@@Table[Cases[primeMS[n],{x_,y_}/;Divisible[y,x]:>x,{0}],{n,1000}]
%Y The divisible pairs are ranked by A318990, proper A339005.
%Y For all semiprimes we have A338912, greater A338913.
%Y The quotient of the pair is A358103.
%Y The reduced version for all semiprimes is A358193, numerator A358192.
%Y A000040 lists the primes.
%Y A001222 counts prime indices, distinct A001221.
%Y A001358 lists the semiprimes, squarefree A006881.
%Y A003963 multiplies together prime indices.
%Y A056239 adds up prime indices.
%Y A318991 ranks divisor-chains.
%Y Cf. A000720, A027751, A128301, A215366, A289508, A289509, A296150, A300912, A318992, A358106.
%K nonn
%O 1,3
%A _Gus Wiseman_, Nov 02 2022
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