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

1,2

Comments

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.

Links

Table of n, a(n) for n=1..55.

Walter Nissen, Primitive Friendly Integers and Exclusive Multiples, Up for the Count!

Eric Weisstein's World of Mathematics, Friendly Pair.

Formula

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

Example

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.

Prog

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

Crossrefs

Cf. A050972, A050973, A165430, A233039.

Sequence in context: A179774 A138918 A071186 * A219041 A218946 A174057

Adjacent sequences: A263115 A263116 A263117 * A263119 A263120 A263121

Keyword

nonn

Author

Michel Marcus, Oct 10 2015

Status

approved