A084190 Least common multiple of {d-1: d > 1 and d divides n}.

1, 1, 2, 3, 4, 10, 6, 21, 8, 36, 10, 330, 12, 78, 28, 105, 16, 680, 18, 684, 60, 210, 22, 53130, 24, 300, 104, 702, 28, 36540, 30, 3255, 160, 528, 204, 157080, 36, 666, 228, 62244, 40, 31980, 42, 9030, 616, 990, 46, 2497110, 48, 3528, 400, 5100, 52, 468520

Offset: 1

Author

Reinhard Zumkeller, May 18 2003

Keywords

• nonn

Comments

Considering the set of divisors > 1 of n reduced by 1, a(n) is the smallest number whose divisors contain this set;

a(n) < n iff n=p^k, p prime and 1 <= k <= 2: a(A001248(n)) < A001248(n), a(A000430(n)) < A000430(n), a(A080257(n))> A080257(n);

a(n) is odd iff n=2^k.

Examples

			n=35: divisors > 1 of 35 = {5,7,35}, a(35) = lcm(4,6,34) = 204;
n=37: divisors > 1 of 37 = {37}, a(37) = lcm(36) = 36.
		

Links

• Carl R. White, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A084191(n) = a(a(n)), A007955.

Cf. A027750.

Cf. A258409.

Programs

Haskell

a084190 1 = 1
a084190 n = foldl1 lcm $ map (subtract 1) $ tail $ a027750_row' n
-- Reinhard Zumkeller, May 08 2012

Mathematica

Join[{1}, Table[LCM @@ (Rest[Divisors[n]] - 1), {n, 2, 100}]] (* T. D. Noe, Apr 25 2012 *)

PARI

a(n)=if(n>2,lcm(apply(k->k-1,vecextract(divisors(n),"2.."))),1) \\ Charles R Greathouse IV, Apr 25 2012

Python

from math import lcm
from sympy import divisors
def A084190(n): return lcm(*(d-1 for d in divisors(n,generator=True) if d > 1)) # Chai Wah Wu, Jun 25 2022

Extensions

a(45) was erroneously split into 61 and 6; repaired by Carl R. White, Apr 25 2012