cp's OEIS Frontend

A355741 Number of ways to choose a sequence of prime factors, one of each prime index of n.

%I A355741 #8 Jul 19 2022 08:04:16
%S A355741 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 A355741 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 A355741 1,0,2,0,2,0,1,0,1,0,2,0,1,0,1,0,1,0,2
%N A355741 Number of ways to choose a sequence of prime factors, one of each prime index of n.
%C A355741 First differs from A355744 at a(169) = 4, A355744(169) = 3.
%C A355741 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 A355741 Wikipedia, <a href="https://en.wikipedia.org/wiki/Cartesian_product">Cartesian product</a>.
%F A355741 Totally multiplicative with a(prime(k)) = A001221(k).
%e A355741 The prime indices of 1131 are {2,6,10}, and the a(1131) = 4 choices are: {2,2,2}, {2,2,5}, {2,3,2}, {2,3,5}.
%t A355741 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A355741 Table[Times@@PrimeNu/@primeMS[n],{n,100}]
%Y A355741 Positions of 0's are A299174.
%Y A355741 The version for all divisors is A355731, firsts A355732.
%Y A355741 Choosing prime-power divisors gives A355742.
%Y A355741 Positions of 1's are A355743.
%Y A355741 Counting multisets instead of sequences gives A355744.
%Y A355741 The weakly increasing case is A355745, all divisors A355735.
%Y A355741 A001414 adds up distinct prime factors, counted by A001221.
%Y A355741 A003963 multiplies together the prime indices of n.
%Y A355741 A056239 adds up prime indices, row sums of A112798, counted by A001222.
%Y A355741 A289509 lists numbers with relatively prime prime indices.
%Y A355741 A324850 lists numbers divisible by the product of their prime indices.
%Y A355741 Cf. A000720, A061395, A076610, A120383, A335433, A355733, A355737, A355739, A355746, A355747.
%K A355741 nonn,mult
%O A355741 1,13
%A A355741 _Gus Wiseman_, Jul 18 2022