cp's OEIS Frontend

A336871 Number of divisors d of A076954(n) with distinct prime multiplicities such that the numerator of A006939(n)/d also has distinct prime multiplicities.

%I A336871 #9 Aug 11 2020 01:50:02
%S A336871 1,2,4,11,28,96,309,1256,4676,21647
%N A336871 Number of divisors d of A076954(n) with distinct prime multiplicities such that the numerator of A006939(n)/d also has distinct prime multiplicities.
%C A336871 The sequence A006939 is A006939(n) = Product_{i = 1..n} prime(i)^(n - i + 1).
%C A336871 The sequence A076954 is A076954(n) = Product_{i=1..n} prime(i)^i.
%e A336871 The a(0) = 1 through a(3) = 11 divisors:
%e A336871   1  2  18   2250
%e A336871      1   9   1125
%e A336871          3    375
%e A336871          1    125
%e A336871                75
%e A336871                45
%e A336871                25
%e A336871                18
%e A336871                 9
%e A336871                 5
%e A336871                 1
%t A336871 chern[n_]:=Product[Prime[i]^(n-i+1),{i,n}];
%t A336871 cochern[n_]:=Product[Prime[i]^i,{i,n}];
%t A336871 Table[Length[Select[Divisors[cochern[n]],UnsameQ@@Last/@FactorInteger[#]&&UnsameQ@@Last/@FactorInteger[chern[n]/#]&]],{n,0,5}]
%Y A336871 A336419 is the version for superprimorials.
%Y A336871 A336500 is the generalization to all positive integers.
%Y A336871 A000005 counts divisors.
%Y A336871 A006939 lists superprimorials or Chernoff numbers.
%Y A336871 A007425 counts divisors of divisors.
%Y A336871 A076954 is a sister of superprimorials.
%Y A336871 A130091 lists numbers with distinct prime multiplicities.
%Y A336871 A181796 counts divisors with distinct prime multiplicities.
%Y A336871 A327523 counts factorizations of elements of A130091 using elements of A130091.
%Y A336871 A336422 counts divisible pairs of divisors, both in A130091.
%Y A336871 A336424 counts factorizations using A130091.
%Y A336871 Cf. A001055, A022559, A022915, A027423, A091050, A124010, A317829, A327498, A327527, A336420, A336421, A336571.
%K A336871 nonn,more
%O A336871 0,2
%A A336871 _Gus Wiseman_, Aug 06 2020