cp's OEIS Frontend

A336421 Number of ways to choose a divisor of a divisor, both having distinct prime exponents, of the n-th superprimorial number A006939(n).

%I A336421 #9 Jul 27 2020 00:24:18
%S A336421 1,3,13,76,571,5309,59341,780149
%N A336421 Number of ways to choose a divisor of a divisor, both having distinct prime exponents, of the n-th superprimorial number A006939(n).
%C A336421 A number has distinct prime exponents iff its prime signature is strict.
%C A336421 The n-th superprimorial or Chernoff number is A006939(n) = Product_{i = 1..n} prime(i)^(n - i + 1).
%e A336421 The a(2) = 13 ways:
%e A336421   12/1/1  12/2/1  12/3/1  12/4/1  12/12/1
%e A336421           12/2/2  12/3/3  12/4/2  12/12/2
%e A336421                           12/4/4  12/12/3
%e A336421                                   12/12/4
%e A336421                                   12/12/12
%t A336421 chern[n_]:=Product[Prime[i]^(n-i+1),{i,n}];
%t A336421 strsig[n_]:=UnsameQ@@Last/@FactorInteger[n];
%t A336421 Table[Total[Cases[Divisors[chern[n]],d_?strsig:>Count[Divisors[d],e_?strsig]]],{n,0,5}]
%Y A336421 A000258 shifted once to the left is dominated by this sequence.
%Y A336421 A336422 is the generalization to non-superprimorials.
%Y A336421 A000110 counts divisors of superprimorials with distinct prime exponents.
%Y A336421 A006939 lists superprimorials or Chernoff numbers.
%Y A336421 A008302 counts divisors of superprimorials by bigomega.
%Y A336421 A022915 counts permutations of prime indices of superprimorials.
%Y A336421 A076954 can be used instead of A006939.
%Y A336421 A130091 lists numbers with distinct prime exponents.
%Y A336421 A181796 counts divisors with distinct prime exponents.
%Y A336421 A181818 gives products of superprimorials.
%Y A336421 A317829 counts factorizations of superprimorials.
%Y A336421 Cf. A000005, A008278, A027423, A071625, A118914, A124010, A327498, A336417, A336419, A336420, A336426, A336500, A336568.
%K A336421 nonn,more
%O A336421 0,2
%A A336421 _Gus Wiseman_, Jul 25 2020