OFFSET
1,1
REFERENCES
Benito, Manuel; Creyaufmueller, Wolfgang; Varona, Juan Luis; and Zimmermann, Paul; Aliquot Sequence 3630 Ends After Reaching 100 Digits; Experimental Mathematics, Vol. 11, No. 2, Natick, MA, 2002, pp. 201-206.
LINKS
Manuel Benito and Juan L. Varona, Advances In Aliquot Sequences, Mathematics of Computation, Vol. 68, No. 225, (1999), pp. 389-393.
Wolfgang Creyaufmueller, Aliquot sequences.
FORMULA
Define s(i)=sigma(i)-i=A000203(i)-i. Then if i is composite and the aliquot sequence obtained by repeatedly applying the mapping i->s(i) contains a prime as a member of its trajectory, i is included in this sequence.
EXAMPLE
a(5)=12 because the fifth composite number whose aliquot sequence terminates by encountering a prime as a member of its trajectory is 12. The complete aliquot sequence generated by iterating the proper divisors of 12 is 12->16->15->9->4->3->1->0
MATHEMATICA
s[n_] := DivisorSigma[1, n] - n; g[n_] := If[n > 0, s[n], 0]; Trajectory[n_] := Most[NestWhileList[g, n, UnsameQ, All]]; Select[Range[2, 275], ! PrimeQ[ # ] && Last[Trajectory[ # ]] == 0 &]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ant King, Jan 06 2007
STATUS
approved