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A263118 Indices of the primitive friendly pairs in the sequence of friendly pairs (A050973, A050972) ordered by smallest maximal element. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 19 14:36 EDT 2020. Contains 337178 sequences. (Running on oeis4.)