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A127161 Integers whose aliquot sequences terminate by encountering a prime number. 4
2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 26, 27, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This sequence is the same as A080907 from A080907's second term onwards.

REFERENCES

Benito, Manuel and Varona, Juan L.; Advances In Aliquot Sequences, Mathematics of Computation, Vol. 68, No. 225, (January 1999), pp. 389-393

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

Table of n, a(n) for n=1..71.

Wolfgang Creyaufmueller, Aliquot sequences.

FORMULA

Define s(i)=sigma(i)-i=A000203(i)-i. Then if the aliquot sequence obtained by repeatedly iterating s contains a prime as a member of its trajectory, i is included in this sequence

EXAMPLE

a(10)=12 because the tenth integer 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], Last[Trajectory[ # ]] == 0 &]

CROSSREFS

Cf. A080907, A127162, A127163, A127164, A098007, A121507, A098008, A007906, A063769, A115060, A115350.

Sequence in context: A054027 A272978 A080907 * A129657 A249407 A103679

Adjacent sequences: A127158 A127159 A127160 * A127162 A127163 A127164

KEYWORD

nonn

AUTHOR

Ant King, Jan 06 2007

STATUS

approved

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Last modified December 9 23:05 EST 2022. Contains 358710 sequences. (Running on oeis4.)