A113901 - OEIS

%I #23 Jan 13 2025 11:25:13

%S 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 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 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 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 a(n) = 1 iff n is prime.

%C A068993(a(n)) = 4. - _Reinhard Zumkeller_, Mar 13 2011

%C Positions of first appearances are A328964. - _Gus Wiseman_, Nov 05 2019

%H G. C. Greubel, <a href="/A113901/b113901.txt">Table of n, a(n) for n = 1..1000</a>

%t Table[PrimeNu[n]*PrimeOmega[n], {n,1,50}] (* _G. C. Greubel_, Apr 23 2017 *)

%o (PARI) a(n) = omega(n)*bigomega(n);

%Y A307409(n) is (bigomega(n) - 1) * omega(n).

%Y A328958(n) is sigma_0(n) - bigomega(n) * omega(n).

%Y Cf. A000005, A001221, A001222, A060687, A070175, A071625, A124010, A303555, A320632, A323023, A328956, A328957, A328964, A328965.

%K easy,nonn

%O 1,4

%A _Cino Hilliard_, Jan 29 2006