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Smallest members of k-sociable cycles of order r, with k > 1 and r > 1.
3

%I #5 Mar 30 2012 18:39:49

%S 5974080,12162100800,90079209000,555108915200

%N Smallest members of k-sociable cycles of order r, with k > 1 and r > 1.

%C A k-sociable (or multisociable) cycle of order r consists of r distinct positive integers such that the sum of the aliquot divisors (or proper divisors) of each is equal to k times the next term in the cycle, where k (the multiplicity) is a fixed positive integer.

%C a(1), a(2) and a(4) are the smallest terms of 2-sociable cycles of order 3 (or bicrowds), and a(3) is the smaller term of a 3-sociable cycle of order 2 (or triamicable pair).

%C No other terms <= 10^12.

%Y Cf. A001065, A166069, A183016, A183020, A183022.

%K nonn,more

%O 1,1

%A _William Rex Marshall_, Jan 08 2011