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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

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Last modified February 20 15:20 EST 2019. Contains 320336 sequences. (Running on oeis4.)