A263152 a(n) is the greatest common unitary divisor of the friendly pairs, A050972(n) and A050973(n).

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

Offset: 1

Author

Michel Marcus, Oct 11 2015

Keywords

• nonn

Comments

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

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

Examples

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

Links

• Michel Marcus, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A050972, A050973, A263118.

Cf. A165430 (greatest common unitary divisor).

Programs

PARI

udivs(n) = {my(d = divisors(n)); select(x->(gcd(x, n/x)==1), d);}
ugcd(x,y) = vecmax(setintersect(udivs(x), udivs(y)));
lista(vp, vg) = {for (n=1, #vp, print1(ugcd(vp[n], vg[n])", ")); } \\ where vp and vg are A050972 and A050973

Formula

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

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