A337074 Number of strict chains of divisors in A130091 (numbers with distinct prime multiplicities), starting with n!.

1, 1, 2, 0, 28, 0, 768, 0, 0, 0, 42155360, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset

0,3

Comments

Support appears to be {0, 1, 2, 4, 6, 10}.

Links

Table of n, a(n) for n=0..83.

Formula

a(n) = 2*A337104(n) = 2*A336423(n!) for n > 1.

Example

The a(4) = 28 chains:
  24  24/1   24/2/1   24/4/2/1   24/8/4/2/1
      24/2   24/3/1   24/8/2/1   24/12/4/2/1
      24/3   24/4/1   24/8/4/1
      24/4   24/4/2   24/8/4/2
      24/8   24/8/1   24/12/2/1
      24/12  24/8/2   24/12/3/1
             24/8/4   24/12/4/1
             24/12/1  24/12/4/2
             24/12/2
             24/12/3
             24/12/4

Mathematica

chnsc[n_]:=If[!UnsameQ@@Last/@FactorInteger[n], {}, If[n==1, {{1}}, Prepend[Join@@Table[Prepend[#, n]&/@chnsc[d], {d, Most[Divisors[n]]}], {n}]]];
Table[Length[chnsc[n!]], {n, 0, 6}]

Crossrefs

A336867 is the complement of the support.

A336868 is the characteristic function (image under A057427).

A336942 is half the version for superprimorials (n > 1).

A337071 does not require distinct prime multiplicities.

A337104 is the case of chains ending with 1.

A000005 counts divisors.

A000142 lists factorial numbers.

A027423 counts divisors of factorial numbers.

A067824 counts chains of divisors starting with n.

A074206 counts chains of divisors from n to 1.

A076716 counts factorizations of factorial numbers.

A130091 lists numbers with distinct prime multiplicities.

A181796 counts divisors with distinct prime multiplicities.

A253249 counts chains of divisors.

A327498 gives the maximum divisor with distinct prime multiplicities.

A336414 counts divisors of n! with distinct prime multiplicities.

A336415 counts divisors of n! with equal prime multiplicities.

A336423 counts chains using A130091, with maximal case A336569.

A336571 counts chains of divisors 1 < d < n using A130091.

Cf. A000110, A001055, A002033, A007489, A022559, A048656, A071626, A098859, A124010, A167865, A325617, A336416, A336424.

Sequence in context: A306416 A327601 A336287 * A156459 A356564 A007218

Adjacent sequences: A337071 A337072 A337073 * A337075 A337076 A337077

Keyword

nonn

Author

Gus Wiseman, Aug 16 2020

Status

approved