[seqfan] Re: Is it certain that this is a permutation?

[Farideh Firoozbakht]

> It seems likely that this is a permutation of the positive integers.
> Is it?

  I think it is true. But I don't know how we can prove it !

  The first 37 terms of A175350 :

  1, 2, 6, 5, 67, 11, 637, 12, 348, 47, 57913, 26, 472366, 463, 26105,
  15, 42488697, 118, 344373650, 136, 2089071, 2496, 30991547417, 7,
  332851440, 93936, 3467844, 590, 22845074981535, 31, 183014339639657,
  13, 13947373787, 1211999, 4542252600361, 91 &  149884187963718221 .

  So the first 37 terms of A175351 are :

  1, 3, 9, 14, 81, 92, 729, 741, 1089, 1136, 59049, 59075, 531441,
  531904, 558009, 558024, 43046721, 43046839, 387420489, 387420625,
  389509696, 389512192, 31381059609, 31381059616, 31713911056,
  31714004992, 31717472836, 31717473426, 22876792454961,
  22876792454992, 205891132094649, 205891132094662, 205905079468449,
  205905080680448, 210447333280809, 210447333280900, 150094635296999121


  I think if p is prime then A175350(p)=3^(p-1)-A175351(p-1).

  ***

  Best wishes,

  Farideh


Quoting Leroy Quet <q1qq2qqq3qqqq at yahoo.com>:

> Just submitted this:
>
> %I A175350
> %S A175350 1,2,6,5,67,11,637
> %N A175350 a(n) = the smallest positive integer not yet occurring   
> such that the number of divisors of sum{k=1 to n} a(k) is exactly n.
> %C A175350 It seems likely that this is a permutation of the   
> positive integers. Is it?
> %C A175350 sum{k=1 to n} a(k) = A175351(n).
> %Y A175350 A175351
> %K A175350 more,nonn
> %O A175350 1,2
>
> Is this for certain a permutation of the positive intgers? Or am I   
> missing something obvious which proves that this is not so?
>
> (PS: I, as I bet Neil does too, hate subjective statements in the   
> comments, such as I have here {..."seems likely"...}. As soon as   
> this sequence appears, if any resolution has been made on this   
> problem, then I will change the comment appropriately.)
>
> Thanks,
> Leroy Quet
>
>
> [ ( [ ([( [ ( ([[o0Oo0Ooo0Oo(0)oO0ooO0oO0o]]) ) ] )]) ] ) ]
>
>
>
>
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>









----------------------------------------------------------------
University of Isfahan (http://www.ui.ac.ir)