computational challenge related to very odd sequences
Don Reble
djr at nk.ca
Sat Jun 26 00:35:46 CEST 2004
> Let S be the set of odd integers n such that ord_2(n) is
> odd, and n has at least one prime divisor p such that
> p^2 does not divide n (e.g. 7^{14}*73, 31*151).
> i_2(n)=sum_{d|n}phi(d)/ord_2(d).
> Let i_2(S)={m: i_2(n)=m for some n in S}
Hmm... you've given that name to two different things.
Still, I think I know what you mean.
> Under the Generalized Riemann Hypothesis it can be shown that
> each number in i_2(S) has an infinite preimage.
> All odd integers <=800 except possibly
> 13,29,37,53,61,149,181,229,293,373,461,541,757,773 are in i_2(S).
> find an integer n in S for which i_2(n) assumes one of the exceptional
> values listed above.
Ok.
i_2(63)=13, i_2(1191)=29, i_2(1649)=37, i_2(585)=53,
i_2(3913)=61, i_2(7695)=149, i_2(13143)=181, i_2(73143)=229,
i_2(4599)=293, i_2(29319)=373, i_2(25025)=461, i_2(77121)=541,
i_2(299831)=757, i_2(64305)=773.
But that looks too easy. Did I get something wrong?
--
Don Reble djr at nk.ca
More information about the SeqFan
mailing list