A233039 -id:A233039 - cp's OEIS frontend

A263118 Indices of the primitive friendly pairs in the sequence of friendly pairs (A050973, A050972) ordered by smallest maximal element.

1, 3, 4, 5, 6, 10, 11, 18, 20, 29, 33, 70, 115, 116, 133, 136, 155, 156, 157, 212, 255, 360, 414, 468, 470, 477, 518, 519, 578, 771, 787, 830, 971, 1039, 1046, 1121, 1687, 1793, 2983, 3092, 3359, 3360, 3570, 4084, 4190, 4255, 5281, 7032, 7141, 7167, 8248, 8385, 8386, 8630, 8890

Offset: 1

Michel Marcus, Oct 10 2015

nonn

Friends x and y are primitive friendly if and only if they have no common prime factor with the same multiplicity, that is, if A165430(x, y) = 1.

			The first pair (6, 28) is primitive since 6=2*3 and 28=2^2*7; their only common prime factor, 2, appears with different exponents, so 1 is a term.
The second pair (30, 140) is not primitive since 30=5*6 and 140=5*28; the prime factor 5 appears in each with the same exponent, so 2 is not a term.

Walter Nissen, Primitive Friendly Integers and Exclusive Multiples, Up for the Count!
Eric Weisstein's World of Mathematics, Friendly Pair.

Cf. A050972, A050973, A165430, A233039.

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, if (ugcd(vp[n], vg[n])==1, print1(n, ", ")););} \\ where vp and vg are A050972 and A050973

A233039(n) = A050973(a(n)).

A290245 Number of larger members of primitive friendly pairs <= 10^n.

Original entry on oeis.org

0, 1, 9, 19, 38, 66, 148, 292, 548, 966, 1688

Offset: 1

Amiram Eldar, Jul 24 2017

a(3)-a(11) were from the paper by Pollack and Pomerance.

Paul Pollack and Carl Pomerance, Some problems of Erdős on the sum-of-divisors function, Transactions of the American Mathematical Society, Series B Vol. 3, No. 1 (2016), pp. 1-26.

Cf. A233039.

cp's OEIS Frontend

A263118 Indices of the primitive friendly pairs in the sequence of friendly pairs (A050973, A050972) ordered by smallest maximal element.

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