cp's OEIS Frontend

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

%I A084190 #26 Jun 25 2022 21:53:38
%S A084190 1,1,2,3,4,10,6,21,8,36,10,330,12,78,28,105,16,680,18,684,60,210,22,
%T A084190 53130,24,300,104,702,28,36540,30,3255,160,528,204,157080,36,666,228,
%U A084190 62244,40,31980,42,9030,616,990,46,2497110,48,3528,400,5100,52,468520
%N A084190 Least common multiple of {d-1: d > 1 and d divides n}.
%C A084190 Considering the set of divisors > 1 of n reduced by 1, a(n) is the smallest number whose divisors contain this set;
%C A084190 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 A084190 a(n) is odd iff n=2^k.
%H A084190 Carl R. White, <a href="/A084190/b084190.txt">Table of n, a(n) for n = 1..10000</a>
%e A084190 n=35: divisors > 1 of 35 = {5,7,35}, a(35) = lcm(4,6,34) = 204;
%e A084190 n=37: divisors > 1 of 37 = {37}, a(37) = lcm(36) = 36.
%t A084190 Join[{1}, Table[LCM @@ (Rest[Divisors[n]] - 1), {n, 2, 100}]] (* _T. D. Noe_, Apr 25 2012 *)
%o A084190 (PARI) a(n)=if(n>2,lcm(apply(k->k-1,vecextract(divisors(n),"2.."))),1) \\ _Charles R Greathouse IV_, Apr 25 2012
%o A084190 (Haskell)
%o A084190 a084190 1 = 1
%o A084190 a084190 n = foldl1 lcm $ map (subtract 1) $ tail $ a027750_row' n
%o A084190 -- _Reinhard Zumkeller_, May 08 2012
%o A084190 (Python)
%o A084190 from math import lcm
%o A084190 from sympy import divisors
%o A084190 def A084190(n): return lcm(*(d-1 for d in divisors(n,generator=True) if d > 1)) # _Chai Wah Wu_, Jun 25 2022
%Y A084190 Cf. A084191(n) = a(a(n)), A007955.
%Y A084190 Cf. A027750.
%Y A084190 Cf. A258409.
%K A084190 nonn
%O A084190 1,3
%A A084190 _Reinhard Zumkeller_, May 18 2003
%E A084190 a(45) was erroneously split into 61 and 6; repaired by _Carl R. White_, Apr 25 2012