A263884 - OEIS

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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

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OFFSET

1,2

COMMENTS

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

LINKS

Table of n, a(n) for n=1..10.

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

FORMULA

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

EXAMPLE

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