login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A336616 Maximum divisor of n! with distinct prime multiplicities. 6
1, 1, 2, 3, 24, 40, 720, 1008, 8064, 72576, 3628800, 5702400, 68428800, 80870400, 317011968, 118879488000, 1902071808000, 2487324672000, 44771844096000, 50039119872000, 1000782397440000, 21016430346240000, 5085976143790080000, 6156707963535360000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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

David A. Corneth, Table of n, a(n) for n = 0..589

Gus Wiseman, Sequences counting and encoding certain classes of multisets

FORMULA

a(n) = A327498(n!).

EXAMPLE

The sequence of terms together with their prime signatures begins:

1: ()

1: ()

2: (1)

3: (1)

24: (3,1)

40: (3,1)

720: (4,2,1)

1008: (4,2,1)

8064: (7,2,1)

72576: (7,4,1)

3628800: (8,4,2,1)

5702400: (8,4,2,1)

68428800: (10,5,2,1)

80870400: (10,5,2,1)

317011968: (11,5,2,1)

118879488000: (11,6,3,2,1)

MATHEMATICA

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

PROG

(PARI) a(n) = { if(n < 2, return(1)); my(pr = primes(primepi(n)), res = pr[#pr]); for(i = 1, #pr, pr[i] = [pr[i], val(n, pr[i])] ); forstep(i = #pr, 2, -1, if(pr[i][2] < pr[i-1][2], res*=pr[i-1][1]^pr[i-1][2] ) ); res }

val(n, p) = my(r=0); while(n, r+=n\=p); r \\ David A. Corneth, Aug 25 2020

CROSSREFS

A327498 is the version not restricted to factorials, with quotient A327499.

A336414 counts these divisors.

A336617 is the quotient n!/a(n).

A336618 is the version for equal prime multiplicities.

A130091 lists numbers with distinct prime multiplicities.

A181796 counts divisors with distinct prime multiplicities.

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

A336415 counts divisors of n! with equal prime multiplicities.

Cf. A000005, A000110, A098859, A118914, A124010, A336424, A336500, A336568.

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

Sequence in context: A032811 A092049 A257789 * A354278 A061778 A160667

Adjacent sequences: A336613 A336614 A336615 * A336617 A336618 A336619

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jul 29 2020

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 27 21:49 EST 2023. Contains 359849 sequences. (Running on oeis4.)