A263884 a(n) = (m(n)*n)! / (n!)^(m(n)+1), where m(n) is the largest prime power <= n.

1, 3, 280, 2627625, 5194672859376, 1903991899429620, 1461034854396267778567973305958400, 450538787986875167583433232345723106006796340625, 146413934927214422927834111686633731590253260933067148964500000000, 3752368324673960479843764075706478869144868251518618794695144146928706880

Offset: 1

Author

Jonathan Sondow, Dec 19 2015

Keywords

• nonn

Comments

Morris and Fritze (2015) prove that a(n) is an integer.

Examples

			The largest prime power <= 6 is m(6) = 5, so a(6) = (5*6)! / (6!)^(5+1) = 30! / (6!)^6 = 1903991899429620.
		

Links

• Howard Carry Morris and Daniel Fritze, Problem 1948, Math. Mag., 88 (2015), 288-289.

Crossrefs

Cf. A057599.

Formula

a(n) = A057599(n) for n a prime power.