A328959 - OEIS

%I #8 Nov 17 2019 16:01:32

%S -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 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 0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0

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

%C Conjecture: All terms are nonnegative except for a(1) = -1.

%H Antti Karttunen, <a href="/A328959/b328959.txt">Table of n, a(n) for n = 1..100000</a>

%H <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>

%F a(n) = A000005(n) - A307408(n). - _Antti Karttunen_, Nov 17 2019

%e a(72) = sigma_0(72) - 2 - (omega(72) - 1) * nu(72) = 12 - 2 - (5 - 1) * 2 = 2.

%t Table[DivisorSigma[0,n]-2-(PrimeOmega[n]-1)*PrimeNu[n],{n,100}]

%o (PARI)

%o A307408(n) = 2+((bigomega(n)-1)*omega(n));

%o A328959(n) = (numdiv(n) - A307408(n)); \\ _Antti Karttunen_, Nov 17 2019

%Y The positions of positive terms are conjectured to be A320632.

%Y Positions of first appearances are A328963.

%Y omega(n) * nu(n) is A113901(n).

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

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

%Y Cf. A000005, A001221, A001222, A112798, A124010, A307408, A323023, A328956, A328960, A328961, A328962, A328965.

%K sign

%O 1,72

%A _Gus Wiseman_, Nov 02 2019. The idea for this sequence came from _Mats Granvik_.