A258324 Least common multiple of all n - d, where d < n and d is a divisor of n.

1, 1, 2, 6, 4, 60, 6, 84, 24, 360, 10, 3960, 12, 1092, 420, 840, 16, 12240, 18, 13680, 1260, 4620, 22, 1275120, 120, 7800, 936, 19656, 28, 1096200, 30, 52080, 5280, 17952, 7140, 5654880, 36, 25308, 8892, 2489760, 40, 1343160, 42, 397320, 27720

Offset: 1

Author

Ivan Neretin, May 26 2015

Keywords

• nonn

Comments

a(n) is a divisor of A072513(n).

a(n) = n-1 if and only if n is prime. - Robert Israel, May 26 2015

Examples

			a(9) = lcm(9-1, 9-3) = lcm(8, 6) = 24.
		

Links

• Ivan Neretin, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A072513 (product instead of LCM).

Cf. A027751.

Programs

Haskell

a258324 n = foldl lcm 1 $ map (n -) $ a027751_row n
-- Reinhard Zumkeller, May 27 2015

Maple

f:= n -> ilcm(seq(n-d, d = numtheory:-divisors(n) minus {n})):
map(f,[$ 1 .. 100]); # Robert Israel, May 26 2015

Mathematica

Table[If[n == 1, 1, LCM @@ (n - Most[Divisors[n]])], {n, 50}]

PARI

a(n)=lcm(apply(d->if(dCharles R Greathouse IV, May 26 2015

Formula

a(n) = lcm(n-d_1, n-d_2, ..., n-d_k) where d_i are the aliquot divisors of n.