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A233039 Larger member of primitive friendly pairs ordered by smallest maximal element. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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).

LINKS

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

EXAMPLE

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.

PROG

(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

CROSSREFS

Cf. A050973, A096366, A214131, A214133.

Sequence in context: A220152 A042526 A184933 * A246902 A236372 A159542

Adjacent sequences:  A233036 A233037 A233038 * A233040 A233041 A233042

KEYWORD

nonn

AUTHOR

Michel Marcus, Dec 03 2013

STATUS

approved

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Last modified February 24 10:35 EST 2020. Contains 332209 sequences. (Running on oeis4.)