cp's OEIS Frontend

A381588 If n = Product (p_j^k_j) then a(n) = Product (lcm(p_j, k_j)), with a(1) = 1.

%I A381588 #20 Mar 02 2025 22:50:08
%S A381588 1,2,3,2,5,6,7,6,6,10,11,6,13,14,15,4,17,12,19,10,21,22,23,18,10,26,3,
%T A381588 14,29,30,31,10,33,34,35,12,37,38,39,30,41,42,43,22,30,46,47,12,14,20,
%U A381588 51,26,53,6,55,42,57,58,59,30,61,62,42,6,65,66,67,34,69,70,71
%N A381588 If n = Product (p_j^k_j) then a(n) = Product (lcm(p_j, k_j)), with a(1) = 1.
%H A381588 Paolo Xausa, <a href="/A381588/b381588.txt">Table of n, a(n) for n = 1..10000</a>
%F A381588 a(p) = p, for p prime.
%e A381588 a(18) = 12 because 18 = 2^1*3^2, lcm(2,1) = 2, lcm(3,2) = 6 and 2*6 = 12.
%e A381588 a(300) = 30 because 300 = 2^2*3^1*5^2, lcm(2,2) = 2, lcm(3,1) = 3, lcm(5,2) = 10 and 2*3*10 = 60.
%t A381588 A381588[n_] := Times @@ LCM @@@ FactorInteger[n];
%t A381588 Array[A381588, 100]
%o A381588 (PARI) a(n) = my(f=factor(n)); prod(i=1, #f~, lcm(f[i,1], f[i,2])); \\ _Michel Marcus_, Mar 02 2025
%Y A381588 Cf. A008473, A008477, A035306, A144338 (fixed points), A369008 (analogous for gcd).
%K A381588 nonn,mult,easy
%O A381588 1,2
%A A381588 _Paolo Xausa_, Feb 28 2025