cp's OEIS Frontend

A337070 Number of strict chains of divisors starting with the superprimorial A006939(n).

%I A337070 #12 Sep 02 2020 23:06:29
%S A337070 1,2,16,1208,1383936,32718467072,20166949856488576,
%T A337070 391322675415566237681536
%N A337070 Number of strict chains of divisors starting with the superprimorial A006939(n).
%C A337070 The n-th superprimorial is A006939(n) = Product_{i = 1..n} prime(i)^(n - i + 1).
%F A337070 a(n) = 2*A336941(n) for n > 0.
%F A337070 a(n) = A067824(A006939(n)).
%e A337070 The a(0) = 1 through a(2) = 16 chains:
%e A337070   1  2    12
%e A337070      2/1  12/1
%e A337070           12/2
%e A337070           12/3
%e A337070           12/4
%e A337070           12/6
%e A337070           12/2/1
%e A337070           12/3/1
%e A337070           12/4/1
%e A337070           12/4/2
%e A337070           12/6/1
%e A337070           12/6/2
%e A337070           12/6/3
%e A337070           12/4/2/1
%e A337070           12/6/2/1
%e A337070           12/6/3/1
%t A337070 chern[n_]:=Product[Prime[i]^(n-i+1),{i,n}];
%t A337070 chnsc[n_]:=If[n==1,{{1}},Prepend[Join@@Table[Prepend[#,n]&/@chnsc[d],{d,Most[Divisors[n]]}],{n}]];
%t A337070 Table[Length[chnsc[chern[n]]],{n,0,3}]
%Y A337070 A022915 is the maximal case.
%Y A337070 A076954 can be used instead of A006939 (cf. A307895, A325337).
%Y A337070 A336571 is the case with distinct prime multiplicities.
%Y A337070 A336941 is the case ending with 1.
%Y A337070 A337071 is the version for factorials.
%Y A337070 A000005 counts divisors.
%Y A337070 A000142 counts divisors of superprimorials.
%Y A337070 A006939 lists superprimorials or Chernoff numbers.
%Y A337070 A067824 counts chains of divisors starting with n.
%Y A337070 A074206 counts chains of divisors from n to 1.
%Y A337070 A253249 counts chains of divisors.
%Y A337070 A317829 counts factorizations of superprimorials.
%Y A337070 Cf. A001055, A002033, A167865, A181818, A336420, A336423, A336942, A337074.
%K A337070 nonn,more
%O A337070 0,2
%A A337070 _Gus Wiseman_, Aug 15 2020