A336617 a(n) = n!/d where d = A336616(n) is the maximum divisor of n! with distinct prime multiplicities.

1, 1, 1, 2, 1, 3, 1, 5, 5, 5, 1, 7, 7, 77, 275, 11, 11, 143, 143, 2431, 2431, 2431, 221, 4199, 4199, 4199, 39083, 39083, 39083, 898909, 898909, 26068361, 26068361, 215441, 2141737, 2141737, 2141737, 66393847, 1009885357, 7953594143, 7953594143, 294282983291

Offset: 0

Author

Gus Wiseman, Jul 29 2020

Keywords

• nonn

Comments

A number's prime signature (row n of A124010) is the sequence of positive exponents in its prime factorization, so a number has distinct prime multiplicities iff all the exponents in its prime signature are distinct.

Examples

			The maximum divisor of 13! with distinct prime multiplicities is 80870400, so a(13) = 13!/80870400 = 77.
		

Links

• Jinyuan Wang, Table of n, a(n) for n = 0..1000
• Gus Wiseman, Sequences counting and encoding certain classes of multisets

Crossrefs

A327499 is the non-factorial generalization, with quotient A327498.

A336414 counts these divisors.

A336616 is the maximum divisor d.

A336619 is the version for equal prime multiplicities.

A130091 lists numbers with distinct prime multiplicities.

A181796 counts divisors with distinct prime multiplicities.

A336415 counts divisors of n! with equal prime multiplicities.

Cf. A000005, A098859, A124010, A336424, A336500, A336568.

Factorial numbers: A000142, A007489, A022559, A027423, A048656, A048742, A071626, A325272, A325273, A325617, A327500, A336416, A336618.

Programs

Mathematica

Table[n!/Max@@Select[Divisors[n!],UnsameQ@@Last/@If[#==1,{},FactorInteger[#]]&],{n,0,15}]

Formula

a(n) = A327499(n!).

Extensions

More terms from Jinyuan Wang, Jul 31 2020