# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/

Search: id:a316978
Showing 1-1 of 1

%I A316978 #6 Jul 18 2018 17:50:59
%S A316978 1,1,1,2,1,1,1,3,2,1,1,4,1,1,1,5,1,4,1,4,1,1,1,7,2,1,3,4,1,1,1,7,1,1,
%T A316978 1,7,1,1,1,7,1,1,1,4,4,1,1,12,2,4,1,4,1,7,1,7,1,1,1,7,1,1,4,11,1,1,1,
%U A316978 4,1,1,1,16,1,1,4,4,1,1,1,12,5,1,1,7,1,1
%N A316978 Number of factorizations of n into factors > 1 with no equivalent primes.
%C A316978 In a factorization, two primes are equivalent if each factor has in its prime factorization the same multiplicity of both primes.
%F A316978 a(prime^n) = A000041(n).
%F A316978 a(squarefree) = 1.
%e A316978 The a(36) = 7 factorizations are (2*2*3*3), (2*2*9), (2*3*6), (3*3*4), (2*18), (3*12), (4*9). Missing from this list are (6*6) and (36).
%t A316978 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A316978 facs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[facs[n/d],Min@@#>=d&]],{d,Rest[Divisors[n]]}]];
%t A316978 dual[eds_]:=Table[First/@Position[eds,x],{x,Union@@eds}];
%t A316978 Table[Length[Select[facs[n],UnsameQ@@dual[primeMS/@#]&]],{n,100}]
%Y A316978 Cf. A001055, A007716, A007717, A020555, A045778, A162247, A281116, A303386.
%Y A316978 Cf. A316974, A316979, A316980, A316981.
%K A316978 nonn
%O A316978 1,4
%A A316978 _Gus Wiseman_, Jul 18 2018

# Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE