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

Author

Cino Hilliard, Jan 29 2006

Keywords

• easy
• nonn

Comments

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

Links

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

Crossrefs

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.

Programs

Mathematica

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

PARI

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

Formula

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