cp's OEIS Frontend

A358193 Denominator of the quotient of the prime indices of the n-th semiprime.

%I A358193 #6 Nov 04 2022 14:44:56
%S A358193 1,2,1,3,4,3,2,5,1,6,5,7,4,8,3,9,1,7,5,4,10,11,2,9,12,5,13,7,14,5,3,
%T A358193 11,15,8,16,6,3,17,7,1,18,13,7,2,19,15,20,6,10,21,11,22,8,9,23,1,17,
%U A358193 24,9,4,7,25,19,26,5,13,27,8,10,28,14,11,29,21,7,30
%N A358193 Denominator of the quotient of the prime indices of the n-th semiprime.
%C A358193 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 A358193 The 31-st semiprime has prime indices (4,6), so the quotient is 4/6 = 2/3; hence a(31) = 3.
%t A358193 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A358193 Denominator/@Divide@@@primeMS/@Select[Range[100],PrimeOmega[#]==2&]
%Y A358193 The divisible pairs are ranked by A318990, proper A339005.
%Y A358193 The unreduced pair is (A338912, A338913).
%Y A358193 The quotients of divisible pairs are A358103.
%Y A358193 The restriction to divisible pairs is A358105, numerator A358104.
%Y A358193 The numerator is A358192.
%Y A358193 A000040 lists the primes.
%Y A358193 A001222 counts prime indices, distinct A001221.
%Y A358193 A001358 lists the semiprimes, squarefree A006881.
%Y A358193 A003963 multiplies together prime indices.
%Y A358193 A056239 adds up prime indices.
%Y A358193 Cf. A000720, A027751, A032741, A128301, A215366, A289508, A289509, A296150, A300912, A318991, A358106.
%K A358193 nonn,frac
%O A358193 1,2
%A A358193 _Gus Wiseman_, Nov 03 2022