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A358104 Unreduced numerator of the n-th divisible pair, where pairs are ordered by Heinz number. Greater prime index of A318990(n).

%I A358104 #9 Jan 27 2023 21:07:38
%S A358104 1,2,2,3,4,4,5,3,6,7,8,6,9,4,8,10,11,6,12,13,14,10,15,16,12,9,17,5,18,
%T A358104 14,8,19,20,21,22,16,23,6,24,18,12,25,26,27,20,28,29,30,15,22,31,12,
%U A358104 32,24,33,34,7,35,36,26,18,37,10,28,38,39,30,40,41,8,42
%N A358104 Unreduced numerator of the n-th divisible pair, where pairs are ordered by Heinz number. Greater prime index of A318990(n).
%C A358104 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 A358104 A358103(n) = a(n)/A358105(n).
%e A358104 The 12th divisible pair is (2,6) so a(12) = 6.
%t A358104 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A358104 Join@@Table[Cases[primeMS[n],{x_,y_}/;Divisible[y,x]:>y,{0}],{n,1000}]
%Y A358104 The divisible pairs are ranked by A318990, proper A339005.
%Y A358104 For all semiprimes we have A338913.
%Y A358104 The quotient of the pair is A358103.
%Y A358104 The denominator is A358105.
%Y A358104 The reduced version for all semiprimes is A358192, denominator A358193.
%Y A358104 A000040 lists the primes.
%Y A358104 A001222 counts prime indices, distinct A001221.
%Y A358104 A001358 lists the semiprimes, squarefree A006881.
%Y A358104 A003963 multiplies together prime indices.
%Y A358104 A056239 adds up prime indices.
%Y A358104 A318991 ranks divisor-chains.
%Y A358104 Cf. A000720, A032741, A128301, A215366, A289508, A289509, A296150, A300912, A318992, A358106.
%K A358104 nonn
%O A358104 1,2
%A A358104 _Gus Wiseman_, Nov 02 2022