cp's OEIS Frontend

A157754 a(1) = 0, a(n) = lcm(A051904(n), A051903(n)) for n >= 2.

%I A157754 #19 Sep 12 2024 07:47:59
%S A157754 0,1,1,2,1,1,1,3,2,1,1,2,1,1,1,4,1,2,1,2,1,1,1,3,2,1,3,2,1,1,1,5,1,1,
%T A157754 1,2,1,1,1,3,1,1,1,2,2,1,1,4,2,2,1,2,1,3,1,3,1,1,1,2,1,1,2,6,1,1,1,2,
%U A157754 1,1,1,6,1,1,2,2,1,1,1,4,4,1,1,2,1,1,1,3,1,2,1,2,1,1,1,5,1,2,2,2
%N A157754 a(1) = 0, a(n) = lcm(A051904(n), A051903(n)) for n >= 2.
%C A157754 a(n) for n >= 2 equals LCM of minimum and maximum exponents in the prime factorization of n.
%C A157754 a(n) for n >= 2 deviates from A072411, first different term is a(360), a(360) = 3, A072411(360) = 6.
%H A157754 Antti Karttunen, <a href="/A157754/b157754.txt">Table of n, a(n) for n = 1..10000</a>
%H A157754 <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>
%H A157754 <a href="/index/Lc#lcm">Index entries for sequences related to lcm's</a>
%F A157754 a(1) = 0, a(p) = 1, a(pq) = 1, a(pq...z) = 1, a(p^k) = k, for p = primes (A000040), pq = product of two distinct primes (A006881), pq...z = product of k (k > 2) distinct primes p, q, ..., z (A120944), p^k = prime powers (A000961(n) for n > 1) k = natural numbers (A000027).
%F A157754 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = A033150. - _Amiram Eldar_, Sep 11 2024
%e A157754 For n = 12 = 2^2 * 3^1 we have a(12) = lcm(2,1) = 2.
%e A157754 For n = 144 = 2^4 * 3^2 we have a(144) = lcm(4,2) = 4.
%t A157754 Table[LCM @@ {Min@ #, Max@ #} - Boole[n == 1] &@ FactorInteger[n][[All, -1]], {n, 100}] (* _Michael De Vlieger_, Jul 12 2017 *)
%o A157754 (PARI) a(n) = if(n == 1, 0, my(e = factor(n)[,2]); lcm(vecmin(e), vecmax(e))); \\ _Amiram Eldar_, Sep 11 2024
%Y A157754 Cf. A000040, A003990, A006881, A033150, A120944, A000961, A000027, A072411, A051904, A051903, A158378.
%K A157754 nonn
%O A157754 1,4
%A A157754 _Jaroslav Krizek_, Mar 05 2009