

A076183


a(n) = the least positive integer k satisfying Omega(k) = Omega(k1)+...+Omega(kn) if such k exists; = 0 otherwise. (Omega(n) (A001222) denotes the number of prime factors of n, counting multiplicity.)


1



3, 3, 4, 1440, 18432, 516096, 2621440, 150994944, 4416602112, 91729428480, 253671505920, 184717953466368, 4714705859903488, 74309393851613184, 1215971899390033920
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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 "kth 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]


LINKS

Table of n, a(n) for n=1..15.


EXAMPLE

k=3 is the least solution of Omega(k) = Omega(k1), so a(1) = 3. k=3 is the least solution of Omega(k) = Omega(k1)+Omega(k2), so a(2) = 3. k=4 is the least solution of Omega(k) = Omega(k1)+Omega(k2)+Omega(k3), so a(3) = 4. k=1440 is the least solution of Omega(k) = Omega(k1)+Omega(k2)+Omega(k3)+Omega(k4), 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

Sequence in context: A306521 A300369 A304296 * A011445 A197137 A133456
Adjacent sequences: A076180 A076181 A076182 * A076184 A076185 A076186


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



