cp's OEIS Frontend

A358105 Unreduced denominator of the n-th divisible pair, where pairs are ordered by Heinz number. Lesser prime index of A318990(n).

%I A358105 #7 Nov 04 2023 13:16:27
%S A358105 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 A358105 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 A358105 1,8,1,3,4,1,1,2,1,1,2,1,3,1,2,1,1,1,1
%N A358105 Unreduced denominator of the n-th divisible pair, where pairs are ordered by Heinz number. Lesser prime index of A318990(n).
%C A358105 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 A358105 A358103(n) = A358104(n)/a(n).
%e A358105 The 12th divisible pair is (2,6) so a(12) = 2.
%t A358105 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A358105 Join@@Table[Cases[primeMS[n],{x_,y_}/;Divisible[y,x]:>x,{0}],{n,1000}]
%Y A358105 The divisible pairs are ranked by A318990, proper A339005.
%Y A358105 For all semiprimes we have A338912, greater A338913.
%Y A358105 The quotient of the pair is A358103.
%Y A358105 The reduced version for all semiprimes is A358193, numerator A358192.
%Y A358105 A000040 lists the primes.
%Y A358105 A001222 counts prime indices, distinct A001221.
%Y A358105 A001358 lists the semiprimes, squarefree A006881.
%Y A358105 A003963 multiplies together prime indices.
%Y A358105 A056239 adds up prime indices.
%Y A358105 A318991 ranks divisor-chains.
%Y A358105 Cf. A000720, A027751, A128301, A215366, A289508, A289509, A296150, A300912, A318992, A358106.
%K A358105 nonn
%O A358105 1,3
%A A358105 _Gus Wiseman_, Nov 02 2022