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

28, 200, 224, 234, 270, 496, 496, 819, 936, 1488, 1638, 3724, 6200, 6200, 6860, 6975, 8128, 8128, 8128, 10976, 13104, 18600, 21600, 24384, 24384, 24800, 27000, 27000, 29792, 40131, 40640, 43008, 50274, 54000, 54400, 58032, 87750, 93100, 154791, 160524

Offset: 1

Author

Michel Marcus, Dec 03 2013

Keywords

• nonn

Comments

Subsequence of A050973.

Friends m and n are primitive friendly if and only if they have no common prime factor of the same multiplicity (see A096366).

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.

PFPs are quite useful to derive new greater amicable pairs from existing ones (see A230148).

Examples

			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.
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.
		

Links

• Donovan Johnson, Table of n, a(n) for n = 1..300

Crossrefs

Cf. A050973, A096366, A214131, A214133.

Programs

PARI

vp(f) = {maxp = f[#f~, 1]; v = vector(primepi(maxp)); for (j=1, #f~, v[primepi(f[j, 1])] = f[j, 2];);v;}
ispfp(vpn, vpi) = {for (k=1, min(#vpn, #vpi), if (vpi[k] && (vpn[k] == vpi[k]), return (0));); return (1);}
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