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A348581 a(n) is the least factor among all the products A307720(k) * A307720(k+1) equal to n.

%I A348581 #10 Oct 25 2021 11:06:44
%S A348581 1,1,1,2,1,2,1,2,3,2,1,3,1,2,3,2,1,3,1,4,3,2,1,3,5,2,3,4,1,5,1,4,3,2,
%T A348581 5,4,1,2,3,5,1,6,1,4,5,2,1,6,7,5,3,4,1,6,5,7,3,2,1,6,1,2,7,8,5,6,1,4,
%U A348581 3,7,1,8,1,2,5,4,7,6,1,8,9,2,1,7,5,2,3
%N A348581 a(n) is the least factor among all the products A307720(k) * A307720(k+1) equal to n.
%C A348581 We know there are n ways to get n as a product of terms A307720(k)*A307720(k+1) for various k's. Look at these 2*n numbers from A307720. Then a(n) is the smallest of them.
%H A348581 Rémy Sigrist, <a href="/A348581/b348581.txt">Table of n, a(n) for n = 1..10000</a>
%H A348581 Rémy Sigrist, <a href="/A348581/a348581.txt">C program for A348581</a>
%F A348581 a(p) = 1 for any prime number p.
%F A348581 a(n) * A348582(n) = n.
%e A348581 For n = 6:
%e A348581 - we have the following products equal to 6:
%e A348581     A307720(7)  * A307720(8)  = 3 * 2 = 6
%e A348581     A307720(12) * A307720(13) = 2 * 3 = 6
%e A348581     A307720(13) * A307720(14) = 3 * 2 = 6
%e A348581     A307720(14) * A307720(15) = 2 * 3 = 6
%e A348581     A307720(15) * A307720(16) = 3 * 2 = 6
%e A348581     A307720(16) * A307720(17) = 2 * 3 = 6
%e A348581 - the corresponding distinct factors are 2 and 3,
%e A348581 - hence a(6) = 2.
%o A348581 (C) See Links section.
%Y A348581 Cf. A307720, A307730, A348582.
%K A348581 nonn
%O A348581 1,4
%A A348581 _Rémy Sigrist_ and _N. J. A. Sloane_, Oct 24 2021