cp's OEIS Frontend

A355737 Number of ways to choose a sequence of divisors, one of each prime index of n (with multiplicity), such that the result has no common divisor > 1.

%I A355737 #11 Jul 18 2022 22:49:49
%S A355737 0,1,1,1,1,2,1,1,3,2,1,2,1,3,4,1,1,4,1,2,4,2,1,2,3,4,7,3,1,4,1,1,4,2,
%T A355737 6,4,1,4,6,2,1,6,1,2,8,3,1,2,5,4,4,4,1,8,4,3,5,4,1,4,1,2,10,1,6,4,1,2,
%U A355737 6,6,1,4,1,6,8,4,6,8,1,2,15,2,1,6,4,4
%N A355737 Number of ways to choose a sequence of divisors, one of each prime index of n (with multiplicity), such that the result has no common divisor > 1.
%C A355737 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 A355737 Wikipedia, <a href="https://en.wikipedia.org/wiki/Coprime_integers">Coprime integers</a>.
%e A355737 The a(2) = 1 through a(18) = 4 choices:
%e A355737   1  1  11  1  11  1  111  11  11  1  111  1  11  11  1111  1  111
%e A355737                12          12  13     112     12  13           112
%e A355737                            21                 14  21           121
%e A355737                                                   23           122
%t A355737 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A355737 Table[Length[Select[Tuples[Divisors/@primeMS[n]],GCD@@#==1&]],{n,100}]
%Y A355737 Dominated by A355731, firsts A355732, primes A355741, prime-powers A355742.
%Y A355737 For weakly increasing instead of coprime we have A355735, primes A355745.
%Y A355737 Positions of first appearances are A355738.
%Y A355737 For strict instead of coprime we have A355739, zeros A355740.
%Y A355737 A000005 counts divisors.
%Y A355737 A001221 counts distinct prime factors, with sum A001414.
%Y A355737 A001222 counts prime factors with multiplicity.
%Y A355737 A003963 multiplies together the prime indices of n.
%Y A355737 A056239 adds up prime indices, row sums of A112798.
%Y A355737 A120383 lists numbers divisible by all of their prime indices.
%Y A355737 A289508 gives GCD of prime indices.
%Y A355737 A289509 ranks relatively prime partitions, odd A302697, squarefree A302796.
%Y A355737 A324850 lists numbers divisible by the product of their prime indices.
%Y A355737 Cf. A000720, A007359, A051424, A076610, A289507, A296150, A302696, A302698, A355733, A355744, A355748.
%K A355737 nonn
%O A355737 1,6
%A A355737 _Gus Wiseman_, Jul 17 2022