OFFSET
1,1
COMMENTS
1. What is the value of a(7)? For n=7, I have not found a solution k less than 10^6. 2. Is a(n) > 0 for all n, i.e. does a solution k to the "k-th Omega recursion" always exist? If not, what is the first n with a(n) = 0?
a(13) <= 4714705859903488. - David Wasserman, Apr 12 2005
a(16) > 2^63. [From Donovan Johnson, Sep 27 2008]
EXAMPLE
k=3 is the least solution of Omega(k) = Omega(k-1), so a(1) = 3. k=3 is the least solution of Omega(k) = Omega(k-1)+Omega(k-2), so a(2) = 3. k=4 is the least solution of Omega(k) = Omega(k-1)+Omega(k-2)+Omega(k-3), so a(3) = 4. k=1440 is the least solution of Omega(k) = Omega(k-1)+Omega(k-2)+Omega(k-3)+Omega(k-4), so a(4) = 1440.
MATHEMATICA
(*Code to find a(6)*) Omega[n_] := Apply[Plus, Transpose[FactorInteger[n]][[2]]]; ub = 10^6; For[i = 2, i <= ub, i++, a[i] = Omega[i]]; start = 8; For[j = start, j <= ub, j++, If[a[j] == a[j - 1] + a[j - 2] + a[j - 3] + a[j - 4] + a[j - 5] + a[j - 6], Print[j]]]
CROSSREFS
KEYWORD
hard,nonn
AUTHOR
Joseph L. Pe, Nov 01 2002
EXTENSIONS
More terms from David Wasserman, Apr 12 2005
a(13)-a(15) from Donovan Johnson, Sep 27 2008
STATUS
approved