

A063769


Aspiring numbers: numbers whose aliquot sequence terminates in a perfect number.


14



25, 95, 119, 143, 417, 445, 565, 608, 650, 652, 675, 685, 783, 790, 909, 913
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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

Table of n, a(n) for n=1..16.
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]] (* JeanFrançois Alcover, Nov 15 2013 *)


CROSSREFS

Cf. A080907, A115350.
Sequence in context: A090659 A010013 A256716 * A099771 A266818 A158547
Adjacent sequences: A063766 A063767 A063768 * A063770 A063771 A063772


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



