[seqfan] A059958

[Don Reble]

Seqfans:

> %N A059958 Smallest number m such that m*(m+1) has n distinct prime factors.

    That could mean "exactly n" or "at least n". Indeed, this
> %F A059958 a(n)=Min{m|A001221(m*(m+1))=n}
    says it's "exactly n". But then, why should we believe this?
> %e A059958 ... a(n)<=A002110(n)-1 because A001221[(q-1)q]>=n+1.
    (q is A002110(n), of course.)
    A002110: primorials; A001221: number of distinct prime factors.

    The two sequences ("exactly n" and "at least n") agree as far as
    we've computed them: perhaps they agree always.

    a(18) = 4339149420605 (5 17 19 31 37 53 193 229)
                    ...06 (2  3  7 11 13 43  47  59 73 83)
    (with either definition. Thanks for the upper bound, Donovan.)


> %N A069354 Lowest base with simple divisibility test for n primes;
>            smallest B such that omega(B) + omega(B-1) = n.

    Here, it's "exactly n". If the other sequence is "exactly n", then
    A069354(n) = A059958(n)+1.

-- 
Don Reble  djr at nk.ca


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