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

1, 2, 16, 1208, 1383936, 32718467072, 20166949856488576, 391322675415566237681536

Offset: 0

Author

Gus Wiseman, Aug 15 2020

Keywords

• nonn
• more

Comments

The n-th superprimorial is A006939(n) = Product_{i = 1..n} prime(i)^(n - i + 1).

Examples

			The a(0) = 1 through a(2) = 16 chains:
  1  2    12
     2/1  12/1
          12/2
          12/3
          12/4
          12/6
          12/2/1
          12/3/1
          12/4/1
          12/4/2
          12/6/1
          12/6/2
          12/6/3
          12/4/2/1
          12/6/2/1
          12/6/3/1
		

Crossrefs

A022915 is the maximal case.

A076954 can be used instead of A006939 (cf. A307895, A325337).

A336571 is the case with distinct prime multiplicities.

A336941 is the case ending with 1.

A337071 is the version for factorials.

A000005 counts divisors.

A000142 counts divisors of superprimorials.

A006939 lists superprimorials or Chernoff numbers.

A067824 counts chains of divisors starting with n.

A074206 counts chains of divisors from n to 1.

A253249 counts chains of divisors.

A317829 counts factorizations of superprimorials.

Cf. A001055, A002033, A167865, A181818, A336420, A336423, A336942, A337074.

Programs

Mathematica

chern[n_]:=Product[Prime[i]^(n-i+1),{i,n}];
chnsc[n_]:=If[n==1,{{1}},Prepend[Join@@Table[Prepend[#,n]&/@chnsc[d],{d,Most[Divisors[n]]}],{n}]];
Table[Length[chnsc[chern[n]]],{n,0,3}]

Formula

a(n) = 2*A336941(n) for n > 0.

a(n) = A067824(A006939(n)).