A336941 Number of strict chains of divisors starting with the superprimorial A006939(n) and ending with 1.

1, 1, 8, 604, 691968, 16359233536, 10083474928244288, 195661337707783118840768, 139988400203593571474134024847360, 4231553868972506381329450624389969130848256, 6090860257621637852755610879241895108657182173073604608, 464479854191019594417264488167571483344961210693790188774166838214656

Offset: 0

Author

Gus Wiseman, Aug 13 2020

Keywords

• nonn

Examples

			The a(2) = 8 chains:
  12/1
  12/2/1
  12/3/1
  12/4/1
  12/6/1
  12/4/2/1
  12/6/2/1
  12/6/3/1
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..25

Crossrefs

A022915 is the maximal case.

A076954 can be used instead of A006939.

A336571 is the case with distinct prime multiplicities.

A336942 is the case using members of A130091.

A337070 is the version ending with any divisor of A006939(n).

A000005 counts divisors.

A074206 counts chains of divisors from n to 1.

A006939 lists superprimorials or Chernoff numbers.

A067824 counts divisor chains starting with n.

A181818 gives products of superprimorials, with complement A336426.

A253249 counts chains of divisors.

A317829 counts factorizations of superprimorials.

A336423 counts chains using A130091, with maximal case A336569.

Cf. A000142, A001055, A002033, A008480, A022559, A027423, A124010, A167865, A181796, A336417, A336420, A337069.

Programs

Mathematica

chern[n_]:=Product[Prime[i]^(n-i+1),{i,n}];
chns[n_]:=If[n==1,1,Sum[chns[d],{d,Most[Divisors[n]]}]];
Table[chns[chern[n]],{n,0,3}]

PARI

a(n)={my(sig=vector(n,i,i), m=vecsum(sig)); sum(k=0, m, prod(i=1, #sig, binomial(sig[i]+k-1, k-1))*sum(r=k, m, binomial(r,k)*(-1)^(r-k)))} \\ Andrew Howroyd, Aug 30 2020

Formula

a(n) = A337070(n)/2 for n > 0.

a(n) = A074206(A006939(n)).

Extensions

Terms a(8) and beyond from Andrew Howroyd, Aug 30 2020