cp's OEIS Frontend

A381614 If n = Product (p_j^k_j) then a(n) = Product (max(p_j, k_j)), with a(1) = 1.

%I A381614 #19 Mar 07 2025 02:55:40
%S A381614 1,2,3,2,5,6,7,3,3,10,11,6,13,14,15,4,17,6,19,10,21,22,23,9,5,26,3,14,
%T A381614 29,30,31,5,33,34,35,6,37,38,39,15,41,42,43,22,15,46,47,12,7,10,51,26,
%U A381614 53,6,55,21,57,58,59,30,61,62,21,6,65,66,67,34,69,70,71,9,73
%N A381614 If n = Product (p_j^k_j) then a(n) = Product (max(p_j, k_j)), with a(1) = 1.
%H A381614 Paolo Xausa, <a href="/A381614/b381614.txt">Table of n, a(n) for n = 1..10000</a>
%F A381614 a(p) = p, for p prime.
%F A381614 Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = A065463 * Product_{p prime} (1 + 1/((p^2-1)*(p^2+p-1)*p^(2*p-2))) = 0.71628338157754073004... . - _Amiram Eldar_, Mar 07 2025
%e A381614 a(18) = 6 because 18 = 2^1*3^2, max(2,1) = 2, max(3,2) = 3 and 2*3 = 6.
%e A381614 a(300) = 30 because 300 = 2^2*3^1*5^2, max(2,2) = 2, max(3,1) = 3, max(5,2) = 5 and 2*3*5 = 30.
%t A381614 A381614[n_] := Times @@ Max @@@ FactorInteger[n];
%t A381614 Array[A381614, 100]
%o A381614 (PARI) a(n) = my(f=factor(n)); prod(i=1, #f~, max(f[i,1], f[i,2])); \\ _Michel Marcus_, Mar 02 2025
%Y A381614 Cf. A008473, A008477, A035306, A065463, A369008, A381588, A381613.
%K A381614 nonn,mult,easy
%O A381614 1,2
%A A381614 _Paolo Xausa_, Mar 01 2025