A066921 -id:A066921 - cp's OEIS frontend

A113901 Product of omega(n) and bigomega(n) = A001221(n)*A001222(n), where omega(x): number of distinct prime divisors of x. bigomega(x): number of prime divisors of x, counted with multiplicity.

0, 1, 1, 2, 1, 4, 1, 3, 2, 4, 1, 6, 1, 4, 4, 4, 1, 6, 1, 6, 4, 4, 1, 8, 2, 4, 3, 6, 1, 9, 1, 5, 4, 4, 4, 8, 1, 4, 4, 8, 1, 9, 1, 6, 6, 4, 1, 10, 2, 6, 4, 6, 1, 8, 4, 8, 4, 4, 1, 12, 1, 4, 6, 6, 4, 9, 1, 6, 4, 9, 1, 10, 1, 4, 6, 6, 4, 9, 1, 10, 4, 4, 1, 12, 4, 4, 4, 8, 1, 12, 4, 6, 4, 4, 4, 12, 1, 6, 6, 8, 1, 9

Offset: 1

Cino Hilliard, Jan 29 2006

Positions of first appearances are A328964. - Gus Wiseman, Nov 05 2019

G. C. Greubel, Table of n, a(n) for n = 1..1000

A307409(n) is (bigomega(n) - 1) * omega(n).
A328958(n) is sigma_0(n) - bigomega(n) * omega(n).
Cf. A000005, A001221, A001222, A060687, A066921, A066922, A068993, A070175, A071625, A124010, A303555, A320632, A323023, A328956, A328957, A328964, A328965.

Table[PrimeNu[n]*PrimeOmega[n], {n,1,50}] (* G. C. Greubel, Apr 23 2017 *)

PARI
```
a(n) = omega(n)*bigomega(n);
```

a(n) = 1 iff n is prime.
A068993(a(n)) = 4. - Reinhard Zumkeller, Mar 13 2011
a(n) = A066921(n)*A066922(n). - Amiram Eldar, May 07 2025

A066922 a(n) = gcd(Omega(n), omega(n)).

Original entry on oeis.org

0, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 2, 2, 1, 2, 1, 2, 1, 1, 1, 3, 1, 1, 2, 2, 2, 2, 1, 2, 2, 2, 1, 3, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 2, 2, 2, 2, 2, 1, 1, 1, 2, 1, 1, 2, 3, 1, 1, 2, 3, 1, 1, 1, 2, 1, 1, 2, 3, 1, 1, 1, 2, 1, 1, 2, 2, 2, 2, 1, 1, 2, 1, 2, 2, 2, 2, 1, 1, 1, 2, 1, 3, 1, 2, 3

Offset: 1

Benoit Cloitre, Jan 23 2002

Harry J. Smith, Table of n, a(n) for n = 1..1000

Cf. A001221 (omega), A001222 (Omega), A066921, A113901.

Table[GCD[PrimeOmega[n],PrimeNu[n]],{n,110}] (* Harvey P. Dale, Dec 05 2015 *)

a(n) = { gcd(bigomega(n),omega(n)) } \\ Harry J. Smith, Apr 07 2010

a(n) = A113901(n)/A066921(n). - Amiram Eldar, May 07 2025

cp's OEIS Frontend

A113901 Product of omega(n) and bigomega(n) = A001221(n)*A001222(n), where omega(x): number of distinct prime divisors of x. bigomega(x): number of prime divisors of x, counted with multiplicity.

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