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

1, 16, 64, 512, 1024, 6561, 16384, 32768, 531441, 2097152, 4194304, 33554432, 67108864, 387420489, 3486784401, 8589934592, 17179869184, 34359738368, 274877906944, 549755813888, 7625597484987, 22876792454961, 70368744177664

Offset: 1

Author

Michel Lagneau, Mar 05 2010

Keywords

• nonn

Comments

bigomega(.) = A001222(.).

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.

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

Examples

			With n = 16 = 2^4, bigomega(16)= 4, bigomega(4)= 2,and 2^4 = 16.
With n = 531441=3^12, bigomega(3^12)= 12, bigomega(12)= 3,and 3^12 = 531441.
		

Crossrefs

Cf. A001222, A167746.

Programs

Maple

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

Extensions

Unspecific references and unrelated cross-references removed - R. J. Mathar, Mar 21 2010