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A233039 Larger member of primitive friendly pairs ordered by smallest maximal element.

%I A233039 #19 Oct 10 2015 16:31:09
%S A233039 28,200,224,234,270,496,496,819,936,1488,1638,3724,6200,6200,6860,
%T A233039 6975,8128,8128,8128,10976,13104,18600,21600,24384,24384,24800,27000,
%U A233039 27000,29792,40131,40640,43008,50274,54000,54400,58032,87750,93100,154791,160524
%N A233039 Larger member of primitive friendly pairs ordered by smallest maximal element.
%C A233039 Subsequence of A050973.
%C A233039 Friends m and n are primitive friendly if and only if they have no common prime factor of the same multiplicity (see A096366).
%C A233039 Perfect numbers greater than 6 (A000396) belong to this sequence as they form primitive friendly pairs (PFPs) with smaller perfect, so that the n-th perfect number will appear n-1 times in the sequence.
%C A233039 PFPs are quite useful to derive new greater amicable pairs from existing ones (see A230148).
%H A233039 Donovan Johnson, <a href="/A233039/b233039.txt">Table of n, a(n) for n = 1..300</a>
%e A233039 28 forms a friendly pair with the lesser integer 6, and this pair cannot be derived from a smaller pair, so it is primitive and 28 belongs to the sequence.
%e A233039 140 forms also a pair with 30, hence 140 belongs to A050973. But the pair (30, 140) can be derived from (6, 28) by multiplying both members by 5, so it is not primitive; hence 140 does not belong to the sequence.
%o A233039 (PARI) vp(f) = {maxp = f[#f~, 1]; v = vector(primepi(maxp)); for (j=1, #f~, v[primepi(f[j, 1])] = f[j, 2];);v;}
%o A233039 ispfp(vpn, vpi) = {for (k=1, min(#vpn, #vpi), if (vpi[k] && (vpn[k] == vpi[k]), return (0));); return (1);}
%o A233039 lista(nn) = {for (n=2, nn, ab = sigma(n)/n; vpn = vp(factor(n)); for (i=2, n-1, if (sigma(i)/i == ab, if (ispfp(vpn, vp(factor(i))), print1(n, ", ")););););} \\ _Michel Marcus_, Dec 03 2013
%Y A233039 Cf. A050973, A096366, A214131, A214133.
%K A233039 nonn
%O A233039 1,1
%A A233039 _Michel Marcus_, Dec 03 2013