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A175209 Numbers n such that bigomega(bigomega(n)) ^ bigomega(n) = n. 0

%I

%S 1,16,64,512,1024,6561,16384,32768,531441,2097152,4194304,33554432,

%T 67108864,387420489,3486784401,8589934592,17179869184,34359738368,

%U 274877906944,549755813888,7625597484987,22876792454961,70368744177664

%N Numbers n such that bigomega(bigomega(n)) ^ bigomega(n) = n.

%C bigomega(.) = A001222(.).

%C There exists an infinity of solutions n of the form n = q^p, where q is prime, bigomega(q^p)= p, and bigomega(p)= q, if we select, for example, p = 2^q.

%C The first solution with q=5 is n=5^32, the first solution with q=7 is n=7^128.

%e With n = 16 = 2^4, bigomega(16)= 4, bigomega(4)= 2,and 2^4 = 16.

%e With n = 531441=3^12, bigomega(3^12)= 12, bigomega(12)= 3,and 3^12 = 531441.

%p with(numtheory): for n from 1 to 1000000000 do: if bigomega(bigomega(n))^bigomega(n)= n then print(n) : fi: od :

%Y Cf. A001222, A167746.

%K nonn

%O 1,2

%A _Michel Lagneau_, Mar 05 2010

%E Unspecific references and unrelated cross-references removed - _R. J. Mathar_, Mar 21 2010

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Last modified March 31 16:23 EDT 2020. Contains 333151 sequences. (Running on oeis4.)