

A085078


The largest number with the prime signature of n! using primes <= n.


0



1, 2, 6, 54, 750, 11250, 360150, 123531450, 3088286250, 64854011250, 77201350992150, 65389544290351050, 32637304517036749530, 2121424793607388719450, 163349709107768931397650
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

n! is the smallest number with that prime signature. E.g. 720 = 2^4*3^2*5. (Can we name a(n) as the eldest brother of n!?) Subsidiary sequence: Total number of distinct numbers with prime signature that of n! having prime divisors less than or equal to n.
Contribution from Reikku Kulon, Sep 18 2008: (Start)
This is n! with prime exponents reversed. Perhaps it should be denoted with an inverted exclamation mark: (inverted!)n
7! = 5040 = 2^4 * 3^2 * 5^1 * 7^1
(inverted!)7 = 360150 = 2^1 * 3^1 * 5^2 * 7^4 (End)


LINKS

Table of n, a(n) for n=1..15.


EXAMPLE

6!= 720 = 2^4*3^2*5, hence a(6) = 5^4*3^2*2 = 11250.
for a(8), 40320= 2^7*3^2*5*7 > 7^7*5^2*3*2 =123531450.


PROG

(PARI) for (n = 1, 20, f = factor(n!); c = matsize(f)[1]; a = prod(i = 1, c, f[i, 1]^f[c + 1  i, 2]); print(a)); (Wasserman)


CROSSREFS

Cf. A000142.
Cf. A000040 [From Reikku Kulon, Sep 18 2008]
Sequence in context: A262046 A280982 A219692 * A152543 A279454 A306021
Adjacent sequences: A085075 A085076 A085077 * A085079 A085080 A085081


KEYWORD

nonn


AUTHOR

Amarnath Murthy, Jul 01 2003


EXTENSIONS

More terms from David Wasserman, Jan 14 2005


STATUS

approved



