2^n-3

[y.kohmoto]

    Hello, seqfans.
    When I calculated -1Sigma perfect number, I factorized many times the
numbers of form 2^n-3.
    Because If m=Product p_i^r_i then -1Sigma(m)=Product(-1+Sum p_k^r_k ,
k=1 to i), so if p_i=2 then -1Sigma(2^n)=2^(n+1)-1-2=2^(n+1)-3.
    And it is necessary to factorize -1Sigma(2^n) for calculating -1Sigma
perfect number.

    s1 : 1, 5, 13, 29, 61, 5, 11, 509, 1021, 5, 4093, 19, 16381, 5, 13
    s2 : 1, 5, 13, 29, 61, 5, 23, 509, 1021, 409, 4093, 431, 16381, 6553, 71
    s3 : 3, 4, 5, 6, 9, 10, 12, 14, 20, 22, 24, 29,
    s4 : 5, 13, 29, 61, 509, 1021, 4093, 16381, 1048573, 4194301, 16777213,
536870909,

    s1 : the smallest prime factor of 2^n-3
    s2 : the greatest prime factor of 2^n-3
    s3 : numbers n such that 2^n-3 is prime
    s4 : primes of form 2^n-3

    s3 already exists on OEIS.

    To Neil :
    Do you need any of them?

    Yasutoshi