A084190 - OEIS

%I #26 Jun 25 2022 21:53:38

%S 1,1,2,3,4,10,6,21,8,36,10,330,12,78,28,105,16,680,18,684,60,210,22,

%T 53130,24,300,104,702,28,36540,30,3255,160,528,204,157080,36,666,228,

%U 62244,40,31980,42,9030,616,990,46,2497110,48,3528,400,5100,52,468520

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

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

%C 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);

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

%H Carl R. White, <a href="/A084190/b084190.txt">Table of n, a(n) for n = 1..10000</a>

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

%e n=37: divisors > 1 of 37 = {37}, a(37) = lcm(36) = 36.

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

%o (PARI) a(n)=if(n>2,lcm(apply(k->k-1,vecextract(divisors(n),"2.."))),1) \\ _Charles R Greathouse IV_, Apr 25 2012

%o (Haskell)

%o a084190 1 = 1

%o a084190 n = foldl1 lcm $ map (subtract 1) $ tail $ a027750_row' n

%o -- _Reinhard Zumkeller_, May 08 2012

%o (Python)

%o from math import lcm

%o from sympy import divisors

%o def A084190(n): return lcm(*(d-1 for d in divisors(n,generator=True) if d > 1)) # _Chai Wah Wu_, Jun 25 2022

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

%Y Cf. A027750.

%Y Cf. A258409.

%K nonn

%O 1,3

%A _Reinhard Zumkeller_, May 18 2003

%E a(45) was erroneously split into 61 and 6; repaired by _Carl R. White_, Apr 25 2012