A336425 Number of ways to choose a divisor with distinct prime exponents of a divisor with distinct prime exponents of n!.

1, 1, 3, 5, 24, 38, 132, 195, 570, 1588, 4193, 6086, 14561, 19232, 37142, 106479, 207291, 266871, 549726, 674330, 1465399, 3086598, 5939574, 7182133, 12324512, 28968994, 46819193, 82873443, 165205159, 196666406, 350397910, 406894074, 593725529, 1229814478, 1853300600, 4024414209, 6049714096, 6968090487, 9700557121, 16810076542, 26339337285

Offset

0,3

Links

Max Alekseyev, Table of n, a(n) for n = 0..85

Example

The a(4) = 24 divisors of divisors:
  1/1  2/1  3/1  4/1  8/1  12/1   24/1
       2/2  3/3  4/2  8/2  12/2   24/2
                 4/4  8/4  12/3   24/3
                      8/8  12/4   24/4
                           12/12  24/8
                                  24/12
                                  24/24

Mathematica

strsigQ[n_]:=UnsameQ@@Last/@FactorInteger[n];
Table[Total[Cases[Divisors[n!], d_?strsigQ:>Count[Divisors[d], e_?strsigQ]]], {n, 0, 20}]

Crossrefs

A336422 is the non-factorial generalization.

A130091 lists numbers with distinct prime exponents.

A181796 counts divisors with distinct prime exponents.

A327526 gives the maximum divisor of n with equal prime exponents.

A327498 gives the maximum divisor of n with distinct prime exponents.

A336414 counts divisors of n! with distinct prime exponents.

A336415 counts divisors of n! with equal prime exponents.

A336423 counts chains in A130091, with maximal version A336569.

Cf. A000005, A000110, A098859, A118914, A124010, A336424, A336500, A336568, A336570, A336571, A336865, A336866, A336869.

Factorial numbers: A000142, A022559, A027423, A048656, A048742, A071626, A325272, A325273, A325617, A327499, A336416, A336418, A336617.

Sequence in context: A005761 A200948 A275148 * A230985 A286427 A290509

Adjacent sequences: A336422 A336423 A336424 * A336426 A336427 A336428

Keyword

nonn

Author

Gus Wiseman, Aug 06 2020

Extensions

Terms a(21) onward from Max Alekseyev, Nov 07 2024

Status

approved