OFFSET
1,1
COMMENTS
There are many numbers whose aliquot sequences have not yet been completely computed, so this sequence is not fully known. In particular, 276 may, perhaps, be an element of this sequence, although this is very unlikely.
Numbers less than 1000 whose aliquot sequence is not known that could possibly be in this sequence are: 276, 306, 396, 552, 564, 660, 696, 780, 828, 888, 966, 996. - Robert Price, Jun 03 2013
REFERENCES
No number terminates at 28, the second perfect number.
LINKS
Eric Weisstein's World of Mathematics, Aspiring Number
EXAMPLE
The divisors of 95 less than itself are 1, 5 and 19. They sum to 25. The divisors of 25 less than itself are 1 and 5. They sum to 6, which is perfect.
MATHEMATICA
perfectQ[n_] := DivisorSigma[1, n] == 2*n; maxAliquot = 10^45; A131884 = {}; s[1] = 1; s[n_] := DivisorSigma[1, n] - n; selQ[n_ /; n <= 5] = False; selQ[n_] := NestWhile[s, n, If[{##}[[-1]] > maxAliquot, Print["A131884: ", n]; AppendTo[A131884, n]; False, Length[{##}] < 4 || {##}[[-4 ;; -3]] != {##}[[-2 ;; -1]]] &, All] // perfectQ; Reap[For[k = 1, k < 1000, k++, If[! perfectQ[k] && selQ[k], Print[k]; Sow[k]]]][[2, 1]] (* Jean-François Alcover, Nov 15 2013 *)
CROSSREFS
KEYWORD
hard,nice,nonn
AUTHOR
Tanya Khovanova and Alexey Radul, Aug 14 2001
EXTENSIONS
a(13)-a(16) from Robert Price, Jun 03 2013
STATUS
approved