A337075 Number of strict chains of divisors in A130091 (numbers with distinct prime multiplicities) starting with a proper divisor of n! and ending with 1.

1, 1, 1, 3, 14, 48, 384, 1308, 40288, 933848, 21077680, 75690016, 5471262080, 7964665440, 54595767744, 17948164982144, 3454946386353664, 5010658671663616, 723456523262697984, 950502767770273280, 165679731871366906880, 8443707247468681128448

Offset: 0

Author

Gus Wiseman, Aug 17 2020

Keywords

• nonn

Examples

			The a(1) = 1 through a(4) = 14 chains (with n! prepended):
  1  2/1  6/1    24/1
          6/2/1  24/2/1
          6/3/1  24/3/1
                 24/4/1
                 24/8/1
                 24/12/1
                 24/4/2/1
                 24/8/2/1
                 24/8/4/1
                 24/12/2/1
                 24/12/3/1
                 24/12/4/1
                 24/8/4/2/1
                 24/12/4/2/1
		

Crossrefs

A336571 is the generalization to not just factorial numbers.

A337104 is the version for chains containing n!.

A000005 counts divisors.

A001055 counts factorizations.

A032741 counts proper divisors.

A071625 counts distinct prime multiplicities.

A074206 counts chains of divisors from n to 1.

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.

A336423 counts chains using A130091, with maximal case A336569.

A336424 counts factorizations using A130091.

A336425 counts divisible pairs of divisors of n!, both in A130091.

Cf. A002033, A098859, A124010, A294068, A327499, A327500, A327523, A337071.

Programs

Mathematica

chnstr[n_]:=If[n==1,1,Sum[chnstr[d],{d,Select[Most[Divisors[n]],UnsameQ@@Last/@FactorInteger[#]&]}]];
Table[chnstr[n!],{n,0,5}]

Formula

a(n) = A337104(n) whenever A337104(n) != 0.

a(n) = A336571(n!).