A177871 Numbers k such that bigomega(k)^omega(k) > k.

60, 120, 210, 420, 840, 1260, 1680, 2310, 2730, 3360, 4620, 5460, 6930, 7140, 9240, 10920, 13860, 14280, 15960, 16380, 18480, 21840, 27720, 28560, 30030, 31920, 32760, 36960, 39270, 43680, 43890, 46410, 55440, 57120, 60060, 73920, 78540, 87360, 87780, 90090, 92820, 103740, 106260

Offset

1,1

Comments

bigomega(n) or Omega(n) is the number of prime divisors of n (counted with multiplicity): A001222, and omega(n) is the number of distinct primes dividing n: A001221.

References

Jean-Marie De Koninck, Ces nombres qui nous fascinent, Entry 60, p. 22, Ellipses, Paris, 2008.

Links

Donovan Johnson, Table of n, a(n) for n = 1..500

Example

120 is in the sequence because bigomega(120) = 5, omega(120) = 3, and 5^3 = 125 > 120.

Maple

with(numtheory): for n from 1 to 200000 do:if bigomega(n)^ nops(factorset(n))>
  n then printf(`%d, `, n):else fi:od:

Mathematica

Select[Range[2, 10^5], PrimeOmega[#]^PrimeNu[#] > # &] (* From Alonso del Arte, Dec 13 2010 *)

Prog

(PARI) is(k) = {my(e = factor(k)[, 2]); vecsum(e)^#e > k; } \\ Amiram Eldar, Sep 12 2024

Crossrefs

Cf. A001221, A001222.

Sequence in context: A334761 A169823 A309842 * A377418 A334382 A337098

Adjacent sequences: A177868 A177869 A177870 * A177872 A177873 A177874

Keyword

nonn

Author

Michel Lagneau, Dec 13 2010

Status

approved