

A127162


Composite numbers whose aliquot sequences terminate by encountering a prime number.


4



4, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 26, 27, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 96, 98, 99
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OFFSET

1,1


REFERENCES

Benito, Manuel and Varona, Juan L.; Advances In Aliquot Sequences, Mathematics of Computation, Vol. 68, No. 225, (1999), pp. 389393.
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. 201206.


LINKS

Table of n, a(n) for n=1..69.
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

Cf. A080907, A127161, A127163, A127164, A098007, A121507, A098008, A007906, A063769, A115060, A115350.
Sequence in context: A267647 A214489 A189207 * A096529 A193166 A155101
Adjacent sequences: A127159 A127160 A127161 * A127163 A127164 A127165


KEYWORD

nonn


AUTHOR

Ant King, Jan 06 2007


STATUS

approved



