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

0,4

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.

Links

Jinyuan Wang, Table of n, a(n) for n = 0..1000

Gus Wiseman, Sequences counting and encoding certain classes of multisets

Formula

a(n) = A327499(n!).

Example

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

Mathematica

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

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.

Sequence in context: A080959 A065548 A152063 * A341865 A347982 A321738

Adjacent sequences: A336614 A336615 A336616 * A336618 A336619 A336620

Keyword

nonn

Author

Gus Wiseman, Jul 29 2020

Extensions

More terms from Jinyuan Wang, Jul 31 2020

Status

approved