[seqfan] Re: N for which Landau's function doesn't give a signature leader

Don Reble djr at nk.ca
Sat Oct 8 10:17:49 CEST 2022

    I doubt Chai Wah Wu's Python program for A000793.
    Can someone test whether it computes a(29) correctly?

> The exceptional values [landau(n) isn't a signature leader] of n begin
> 3, 8, 9, 14, 15, 16, 25, 26, 27, 32, 33, 38, 39, 42, 57 ...
    landau(25), landau(26) are signature leaders.

> Research questions:
    Some questions can be answered by scanning the b-files.
    (But I haven't verified those.)
> Are there an infinite number of exceptions?
    The "exceptional" values seem to be more common than the rest.
    Of the first 40001 values, only 8772 are signature leaders (A025487).

> do all the exceptions consist of a signature leader times one or two
> larger primes?
    landau(640) is a 53-smooth signature leader times 61*67*73.
    The extra primes needn't be consecutive.

    The extra primes can be small.
    landau(36548) is a 647-smooth signature leader times 19*659.

Don Reble  djr at nk.ca

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