A337104 Number of strict chains of divisors from n! to 1 using terms of A130091 (numbers with distinct prime multiplicities).

1, 1, 1, 0, 14, 0, 384, 0, 0, 0, 21077680, 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

Author

Gus Wiseman, Aug 17 2020

Keywords

• nonn

Comments

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

Examples

			The a(4) = 14 chains:
  24/1
  24/2/1
  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

A336867 appears to be the positions of zeros.

A336868 is the characteristic function (image under A057427).

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

A337105 does not require distinct prime multiplicities.

A337074 does not require chains to end with 1.

A337075 is the version for chains not containing n!.

A000005 counts divisors.

A000142 lists factorial numbers.

A001055 counts factorizations.

A027423 counts divisors of factorial numbers.

A067824 counts chains of divisors starting with n.

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.

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

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

A337071 counts chains of divisors starting with n!.

Cf. A002033, A022559, A071626, A098859, A124010, A167865, A327523, A336424, A336941.

Programs

Mathematica

strchns[n_]:=If[n==1,1,If[!UnsameQ@@Last/@FactorInteger[n],0,Sum[strchns[d],{d,Select[DeleteCases[Divisors[n],n],UnsameQ@@Last/@FactorInteger[#]&]}]]];
Table[strchns[n!],{n,0,8}]

Formula

a(n) = A337075(n) whenever A337075(n) != 0.

a(n) = A337074(n)/2 for n > 1.

a(n) = A336423(n!).