|
|
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
|
|
|
FORMULA
|
|
|
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 }
|
|
CROSSREFS
|
A327498 is the version not restricted to factorials, with quotient A327499.
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.
Factorial numbers: A000142, A007489, A022559, A027423, A048656, A048742, A071626, A325272, A325273, A325617, A336416.
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|