cp's OEIS Frontend

A355744 Number of multisets that can be obtained by choosing a prime factor of each prime index of n.

%I A355744 #6 Jul 19 2022 08:04:12
%S A355744 1,0,1,0,1,0,1,0,1,0,1,0,2,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,2,0,1,0,1,0,
%T A355744 1,0,2,0,2,0,1,0,2,0,1,0,2,0,1,0,1,0,1,0,1,0,1,0,1,0,2,0,1,0,2,0,1,0,
%U A355744 1,0,2,0,2,0,1,0,1,0,2,0,1,0,1,0,1,0,2
%N A355744 Number of multisets that can be obtained by choosing a prime factor of each prime index of n.
%C A355744 First differs from A355741 at a(169) = 3, A355741(169) = 4.
%C A355744 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.
%H A355744 Wikipedia, <a href="https://en.wikipedia.org/wiki/Axiom_of_choice">Axiom of choice</a>.
%e A355744 The a(169) = 3 multisets are: {2,2}, {2,3}, {3,3}.
%e A355744 The a(507) = 3 multisets are: {2,2,2}, {2,2,3}, {2,3,3}.
%t A355744 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A355744 Table[Length[Union[Sort/@Tuples[primeMS/@primeMS[n]]]],{n,100}]
%Y A355744 Choosing from all divisors gives A355733, firsts A355734.
%Y A355744 Counting sequences instead of multisets gives A355741.
%Y A355744 Choosing weakly increasing sequences of divisors gives A355745.
%Y A355744 A001414 adds up distinct prime divisors, counted by A001221.
%Y A355744 A003963 multiplies together the prime indices of n.
%Y A355744 A056239 adds up prime indices, row sums of A112798, counted by A001222.
%Y A355744 A324850 lists numbers divisible by the product of their prime indices.
%Y A355744 A344606 counts alternating permutations of prime indices.
%Y A355744 Cf. A000720, A076610, A120383, A289509, A335433, A340852, A355731, A355735, A355737, A355739, A355740.
%K A355744 nonn
%O A355744 1,13
%A A355744 _Gus Wiseman_, Jul 18 2022