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%I A336500 #16 Sep 02 2020 23:04:49
%S A336500 1,2,2,3,2,2,2,4,3,2,2,4,2,2,2,5,2,4,2,4,2,2,2,6,3,2,4,4,2,0,2,6,2,2,
%T A336500 2,6,2,2,2,6,2,0,2,4,4,2,2,8,3,4,2,4,2,6,2,6,2,2,2,4,2,2,4,7,2,0,2,4,
%U A336500 2,0,2,8,2,2,4,4,2,0,2,8,5,2,2,4,2,2,2
%N A336500 Number of divisors d|n with distinct prime multiplicities such that the quotient n/d also has distinct prime multiplicities.
%C A336500 A number's prime signature (row n of A124010) is the sequence of positive exponents in its prime factorization, so a number has distinct prime multiplicities iff all the exponents in its prime signature are distinct.
%e A336500 The a(1) = 1 through a(16) = 5 divisors:
%e A336500   1  1  1  1  1  2  1  1  1  2  1  1  1  2  3  1
%e A336500      2  3  2  5  3  7  2  3  5 11  3 13  7  5  2
%e A336500            4           4  9        4           4
%e A336500                        8          12           8
%e A336500                                               16
%t A336500 Table[Length[Select[Divisors[n],UnsameQ@@Last/@FactorInteger[#]&&UnsameQ@@Last/@FactorInteger[n/#]&]],{n,25}]
%Y A336500 A336419 is the version for superprimorials.
%Y A336500 A336568 gives positions of zeros.
%Y A336500 A336869 is the restriction to factorials.
%Y A336500 A007425 counts divisors of divisors.
%Y A336500 A056924 counts divisors greater than their quotient.
%Y A336500 A074206 counts chains of divisors from n to 1.
%Y A336500 A130091 lists numbers with distinct prime exponents.
%Y A336500 A181796 counts divisors with distinct prime multiplicities.
%Y A336500 A336424 counts factorizations using A130091.
%Y A336500 A336422 counts divisible pairs of divisors, both in A130091.
%Y A336500 A327498 gives the maximum divisor with distinct prime multiplicities.
%Y A336500 A336423 counts chains in A130091, with maximal version A336569.
%Y A336500 A336568 gives numbers not a product of two elements of A130091.
%Y A336500 A336571 counts divisor sets using A130091, with maximal version A336570.
%Y A336500 Cf. A000005, A001055, A002033, A098859, A124010, A167865, A253249, A336870.
%K A336500 nonn
%O A336500 1,2
%A A336500 _Gus Wiseman_, Aug 06 2020

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