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%I #14 Oct 12 2015 12:03:47
%S 1,3,4,5,6,10,11,18,20,29,33,70,115,116,133,136,155,156,157,212,255,
%T 360,414,468,470,477,518,519,578,771,787,830,971,1039,1046,1121,1687,
%U 1793,2983,3092,3359,3360,3570,4084,4190,4255,5281,7032,7141,7167,8248,8385,8386,8630,8890
%N Indices of the primitive friendly pairs in the sequence of friendly pairs (A050973, A050972) ordered by smallest maximal element.
%C 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.
%H Walter Nissen, <a href="http://upforthecount.com/math/mandrill.html">Primitive Friendly Integers and Exclusive Multiples</a>, Up for the Count!
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/FriendlyPair.html">Friendly Pair</a>.
%F A233039(n) = A050973(a(n)).
%e 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.
%e 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.
%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, if (ugcd(vp[n], vg[n])==1, print1(n, ", ")););} \\ where vp and vg are A050972 and A050973
%Y Cf. A050972, A050973, A165430, A233039.
%K nonn
%O 1,2
%A _Michel Marcus_, Oct 10 2015
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