A167746 -id:A167746 - cp's OEIS frontend

A176029 a(n)= n^Omega(n).

1, 2, 3, 16, 5, 36, 7, 512, 81, 100, 11, 1728, 13, 196, 225, 65536, 17, 5832, 19, 8000, 441, 484, 23, 331776, 625, 676, 19683, 21952, 29, 27000, 31, 33554432, 1089, 1156, 1225, 1679616, 37, 1444, 1521, 2560000, 41, 74088, 43, 85184, 91125, 2116, 47

Offset: 1

Michel Lagneau, Apr 06 2010, corrected Jul 07 2012

			a(1) = 1^0 = 1 ; a(2) = 2^1 = 2 ; a(3) = 3^1 = 3 ; a(4) = 4^2 = 16 ; a(12) = 12^3 = 1728.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A001222, A167746.

A176029 := proc(n)
      n^numtheory[bigomega](n) ;
end proc: # R. J. Mathar, Jul 08 2012

Array[ #^Plus @@ Last /@ FactorInteger[ # ] &, 105]
PrimeOmega[Range[120]] (* Jul 07 2012 *)

a(n) = n^A001222(n).

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

Original entry on oeis.org

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

Michel Lagneau, Mar 05 2010

nonn

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.

			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.

Cf. A001222, A167746.

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

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

cp's OEIS Frontend

A176029 a(n)= n^Omega(n).

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