[seqfan] Re: d(a(n)) = d(a(n)-a(n-1))

[Farideh Firoozbakht]

Quoting Leroy Quet <q1qq2qqq3qqqq at yahoo.com>:

>
> Consider these three sequences I just submitted:
>
> %I A160689
> %S A160689 1,2,2,2,8,2,2,8,2,2,8,2,2,8,2,21,5
> %N A160689 a(1)=1. a(n) = the smallest positive integer such that   
> d(a(n)) = d(sum{k=1 to n} a(k)), where d(m) = the number of divisors  
>  of m.
> %C A160689 sum{k=1 to n} a(k) = A160690(n). d(A160689(n)) =   
> d(A160690(n)) = A160691(n).
> %Y A160689 A160690,A160691
> %K A160689 more,nonn
> %O A160689 1,2
>
> %I A160690
> %S A160690 1,3,5,7,15,17,19,27,29,31,39,41,43,51,53,74,79
> %N A160690 a(1)=1. a(n) = the smallest integer > a(n-1) such that  
>  d(a(n)) = d(a(n)-a(n-1)), where d(m) = the number of divisors of m.
> %C A160690 A160690(n)-A160690(n-1) = A160689(n), for n >= 2.   
> d(A160689(n)) = d(A160690(n)) = A160691(n).
> %Y A160690 A160689,A160691
> %K A160690 more,nonn
> %O A160690 1,2
>
> %I A160691
> %S A160691 1,2,2,2,4,2,2,4,2,2,4,2,2,4,2,4,2
> %N A160691 a(n) = the number of divisors of A160689(n) = the number   
> of divisors of A160690(n).
> %Y A160691 A160689,A160690
> %K A160691 more,nonn
> %O A160691 1,2
>
> Does every positive integer occur in A160691?
>
> If so, could someone calculate a few of the terms of the sequence   
> {b(k)},T where b(n) = the smallest positive integer such that   
> A160691(b(n)) = n?
>
> Thanks,
> Leroy Quet
>
>
>
>
>
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