A258324 - OEIS

%I #16 Mar 13 2018 04:08:37

%S 1,1,2,6,4,60,6,84,24,360,10,3960,12,1092,420,840,16,12240,18,13680,

%T 1260,4620,22,1275120,120,7800,936,19656,28,1096200,30,52080,5280,

%U 17952,7140,5654880,36,25308,8892,2489760,40,1343160,42,397320,27720

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

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

%C a(n) = n-1 if and only if n is prime. - _Robert Israel_, May 26 2015

%H Ivan Neretin, <a href="/A258324/b258324.txt">Table of n, a(n) for n = 1..1000</a>

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

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

%p f:= n -> ilcm(seq(n-d, d = numtheory:-divisors(n) minus {n})):

%p map(f,[$ 1 .. 100]); # _Robert Israel_, May 26 2015

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

%o (PARI) a(n)=lcm(apply(d->if(d<n,n-d,1),divisors(n))) \\ _Charles R Greathouse IV_, May 26 2015

%o (Haskell)

%o a258324 n = foldl lcm 1 $ map (n -) $ a027751_row n

%o -- _Reinhard Zumkeller_, May 27 2015

%Y Cf. A072513 (product instead of LCM).

%Y Cf. A027751.

%K nonn

%O 1,3

%A _Ivan Neretin_, May 26 2015