A263152 - OEIS

%I #10 Oct 13 2015 04:01:14

%S 1,5,1,1,1,1,11,13,17,1,1,19,3,23,3,25,29,1,31,1,37,41,5,43,47,7,53,3,

%T 1,55,7,2,1,59,61,9,65,67,71,9,73,11,79,83,85,11,5,5,89,11,13,95,97,

%U 101,103,13,11,107,109,113,115,4,121,17,7,125,13,127,131

%N a(n) is the greatest common unitary divisor of the friendly pairs, A050972(n) and A050973(n).

%C Dividing both A050972(n) and A050973(n) by a "greater than 1" divisor of a(n), if any, will give a smaller friendly pair.

%C If a(n) is greater than 1, dividing both A050972(n) and A050973(n) will give a primitive friendly pair.

%H Michel Marcus, <a href="/A263152/b263152.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A165430(A050972(n), A050973(n)).

%F a(A263118(n)) = 1, the primitive friendly pairs.

%e The greatest common unitary divisor of the first friendly pair (6, 28) is 1, hence a(1) = 1.

%o (PARI) udivs(n) = {my(d = divisors(n)); select(x->(gcd(x, n/x)==1), d);}

%o ugcd(x,y) = vecmax(setintersect(udivs(x), udivs(y)));

%o lista(vp, vg) = {for (n=1, #vp, print1(ugcd(vp[n], vg[n]), ", ")); ); } \\ where vp and vg are A050972 and A050973

%Y Cf. A050972, A050973, A263118.

%Y Cf. A165430 (greatest common unitary divisor).

%K nonn

%O 1,2

%A _Michel Marcus_, Oct 11 2015