cp's OEIS Frontend

A328959 a(n) = sigma_0(n) - 2 - (omega(n) - 1) * nu(n), where sigma_0 = A000005, nu = A001221, omega = A001222.

%I A328959 #10 Jul 09 2025 04:49:38
%S A328959 -1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%T A328959 0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,
%U A328959 0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0
%N A328959 a(n) = sigma_0(n) - 2 - (omega(n) - 1) * nu(n), where sigma_0 = A000005, nu = A001221, omega = A001222.
%C A328959 Conjecture: All terms are nonnegative except for a(1) = -1.
%H A328959 Antti Karttunen, <a href="/A328959/b328959.txt">Table of n, a(n) for n = 1..100000</a>
%H A328959 <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>
%F A328959 a(n) = A000005(n) - A307408(n). - _Antti Karttunen_, Nov 17 2019
%e A328959 a(72) = sigma_0(72) - 2 - (omega(72) - 1) * nu(72) = 12 - 2 - (5 - 1) * 2 = 2.
%t A328959 Table[DivisorSigma[0,n]-2-(PrimeOmega[n]-1)*PrimeNu[n],{n,100}]
%o A328959 (PARI)
%o A328959 A307408(n) = 2+((bigomega(n)-1)*omega(n));
%o A328959 A328959(n) = (numdiv(n) - A307408(n)); \\ _Antti Karttunen_, Nov 17 2019
%Y A328959 The positions of positive terms are conjectured to be A320632.
%Y A328959 Positions of first appearances are A328963.
%Y A328959 omega(n) * nu(n) is A113901(n).
%Y A328959 (omega(n) - 1) * nu(n) is A307409.
%Y A328959 sigma_0(n) - omega(n) * nu(n) is A328958(n).
%Y A328959 Cf. A000005, A001221, A001222, A112798, A124010, A307408, A323023, A328956, A328960, A328961, A328962, A328965.
%K A328959 sign
%O A328959 1,72
%A A328959 _Gus Wiseman_, Nov 02 2019. The idea for this sequence came from _Mats Granvik_