A336942 Number of strict chains of divisors in A130091 (numbers with distinct prime multiplicities) starting with the superprimorial A006939(n) and ending with 1.

1, 1, 5, 95, 8823, 4952323, 20285515801, 714092378624317

Offset: 0

Author

Gus Wiseman, Aug 14 2020

Keywords

• nonn
• more

Examples

			The a(0) = 1 through a(2) = 5 chains:
  {1}  {2,1}  {12,1}
              {12,2,1}
              {12,3,1}
              {12,4,1}
              {12,4,2,1}
		

Crossrefs

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

A336423 and A336571 are not restricted to A006939.

A336941 is the version not restricted by A130091.

A337075 is the version for factorials.

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.

A336422 counts divisible pairs of divisors, both in A130091.

A336424 counts factorizations using A130091.

Cf. A000005, A001055, A002033, A032741, A067824, A124010, A167865, A336419, A336420, A336500, A336568.

Programs

Mathematica

chern[n_]:=Product[Prime[i]^(n-i+1),{i,n}];
chnstr[n_]:=If[n==1,1,Sum[chnstr[d],{d,Select[Most[Divisors[n]],UnsameQ@@Last/@FactorInteger[#]&]}]];
Table[chnstr[chern[n]],{n,0,3}]

Formula

a(n) = A336423(A006939(n)) = A336571(A006939(n)).