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.

%I A113901 #29 May 07 2025 03:03:58
%S A113901 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,
%T A113901 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,
%U A113901 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
%N 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.
%C A113901 Positions of first appearances are A328964. - _Gus Wiseman_, Nov 05 2019
%H A113901 G. C. Greubel, <a href="/A113901/b113901.txt">Table of n, a(n) for n = 1..1000</a>
%F A113901 a(n) = 1 iff n is prime.
%F A113901 A068993(a(n)) = 4. - _Reinhard Zumkeller_, Mar 13 2011
%F A113901 a(n) = A066921(n)*A066922(n). - _Amiram Eldar_, May 07 2025
%t A113901 Table[PrimeNu[n]*PrimeOmega[n], {n,1,50}] (* _G. C. Greubel_, Apr 23 2017 *)
%o A113901 (PARI) a(n) = omega(n)*bigomega(n);
%Y A113901 A307409(n) is (bigomega(n) - 1) * omega(n).
%Y A113901 A328958(n) is sigma_0(n) - bigomega(n) * omega(n).
%Y A113901 Cf. A000005, A001221, A001222, A060687, A066921, A066922, A068993, A070175, A071625, A124010, A303555, A320632, A323023, A328956, A328957, A328964, A328965.
%K A113901 easy,nonn
%O A113901 1,4
%A A113901 _Cino Hilliard_, Jan 29 2006