cp's OEIS Frontend

A355739 Number of ways to choose a sequence of all different divisors, one of each prime index of n (with multiplicity).

%I A355739 #7 Jul 19 2022 08:04:21
%S A355739 1,1,2,0,2,1,3,0,2,1,2,0,4,2,3,0,2,0,4,0,4,1,3,0,2,3,0,0,4,1,2,0,3,1,
%T A355739 5,0,6,3,6,0,2,1,4,0,2,2,4,0,6,0,3,0,5,0,3,0,6,3,2,0,6,1,2,0,6,1,2,0,
%U A355739 5,2,6,0,4,5,2,0,5,2,4,0,0,1,2,0,3,3,6
%N A355739 Number of ways to choose a sequence of all different divisors, one of each prime index of n (with multiplicity).
%C A355739 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 A355739 Wikipedia, <a href="https://en.wikipedia.org/wiki/Cartesian_product">Cartesian product</a>.
%e A355739 The a(49) = 6 ways are: (1,2), (1,4), (2,1), (2,4), (4,1), (4,2).
%e A355739 The a(182) = 5 ways are: (1,2,3), (1,2,6), (1,4,2), (1,4,3), (1,4,6).
%e A355739 The a(546) = 2 ways are: (1,2,4,3), (1,2,4,6).
%t A355739 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A355739 Table[Length[Select[Tuples[Divisors/@primeMS[n]],UnsameQ@@#&]],{n,100}]
%Y A355739 This is the strict version of A355731, firsts A355732.
%Y A355739 For relatively prime instead of strict we have A355737, firsts A355738.
%Y A355739 Positions of 0's are A355740.
%Y A355739 A000005 counts divisors.
%Y A355739 A001221 counts distinct prime factors, with sum A001414.
%Y A355739 A001222 counts prime factors with multiplicity.
%Y A355739 A003963 multiplies together the prime indices of n.
%Y A355739 A056239 adds up prime indices, row sums of A112798.
%Y A355739 A120383 lists numbers divisible by all of their prime indices.
%Y A355739 A289508 gives GCD of prime indices, positions of 1's A289509.
%Y A355739 Cf. A000720, A076610, A302796, A355535, A355537, A355733, A355735, A355741, A355742, A355744, A355748.
%K A355739 nonn
%O A355739 1,3
%A A355739 _Gus Wiseman_, Jul 18 2022