cp's OEIS Frontend

A358192 Numerator of the quotient of the prime indices of the n-th semiprime.

%I A358192 #10 Jul 15 2023 10:36:08
%S A358192 1,1,1,1,1,2,1,1,1,1,2,1,3,1,1,1,1,2,3,1,1,1,1,2,1,4,1,3,1,1,2,2,1,3,
%T A358192 1,1,1,1,4,1,1,2,1,1,1,2,1,5,3,1,3,1,1,4,1,1,2,1,1,1,5,1,2,1,2,3,1,5,
%U A358192 1,1,3,4,1,2,6,1,1,1,3,2,5,1,1,1,3,1,1
%N A358192 Numerator of the quotient of the prime indices of the n-th semiprime.
%C A358192 A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
%e A358192 The 31st semiprime has prime indices (4,6), so the quotient is 4/6 = 2/3; hence a(31) = 2.
%t A358192 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A358192 Numerator/@Divide@@@primeMS/@Select[Range[100],PrimeOmega[#]==2&]
%Y A358192 The divisible pairs are ranked by A318990, proper A339005.
%Y A358192 The unreduced pair is (A338912, A338913).
%Y A358192 The quotients of divisible pairs are A358103.
%Y A358192 The restriction to divisible pairs is A358104, denominator A358105.
%Y A358192 The denominator is A358193.
%Y A358192 A000040 lists the primes.
%Y A358192 A001222 counts prime indices, distinct A001221.
%Y A358192 A001358 lists the semiprimes, squarefree A006881.
%Y A358192 A003963 multiplies together prime indices.
%Y A358192 A056239 adds up prime indices.
%Y A358192 Cf. A000720, A027751, A128301, A215366, A289508, A289509, A296150, A300912, A318991, A358106.
%K A358192 nonn,frac
%O A358192 1,6
%A A358192 _Gus Wiseman_, Nov 03 2022