cp's OEIS Frontend

A381613 If n = Product (p_j^k_j) then a(n) = Product (min(p_j, k_j)), with a(1) = 1.

%I A381613 #20 Mar 07 2025 02:55:43
%S A381613 1,1,1,2,1,1,1,2,2,1,1,2,1,1,1,2,1,2,1,2,1,1,1,2,2,1,3,2,1,1,1,2,1,1,
%T A381613 1,4,1,1,1,2,1,1,1,2,2,1,1,2,2,2,1,2,1,3,1,2,1,1,1,2,1,1,2,2,1,1,1,2,
%U A381613 1,1,1,4,1,1,2,2,1,1,1,2,3,1,1,2,1,1,1,2,1,2,1
%N A381613 If n = Product (p_j^k_j) then a(n) = Product (min(p_j, k_j)), with a(1) = 1.
%C A381613 First differs from A323308 at n = 27.
%H A381613 Paolo Xausa, <a href="/A381613/b381613.txt">Table of n, a(n) for n = 1..10000</a>
%F A381613 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Product_{p prime} (1 + (1/p - 1/p^p)/(p-1)) = 1.59383299054679951264... . - _Amiram Eldar_, Mar 07 2025
%e A381613 a(18) = 2 because 18 = 2^1*3^2, min(2,1) = 1, min(3,2) = 2 and 1*2 = 2.
%e A381613 a(300) = 4 because 300 = 2^2*3^1*5^2, min(2,2) = 2, min(3,1) = 1, min(5,2) = 2 and 2*1*2 = 4.
%t A381613 A381613[n_] := Times @@ Min @@@ FactorInteger[n];
%t A381613 Array[A381613, 100]
%o A381613 (PARI) a(n) = my(f=factor(n)); prod(i=1, #f~, min(f[i,1], f[i,2])); \\ _Michel Marcus_, Mar 02 2025
%Y A381613 Cf. A008473, A008477, A035306, A323308, A369008, A381588, A381614.
%K A381613 nonn,mult,easy
%O A381613 1,4
%A A381613 _Paolo Xausa_, Mar 01 2025