A328958 - OEIS

%I #13 Jan 27 2025 16:45:30

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

%T 0,1,1,0,0,0,1,-1,1,0,0,0,1,0,1,0,0,0,1,0,0,0,0,0,1,0,1,0,0,1,0,-1,1,

%U 0,0,-1,1,2,1,0,0,0,0,-1,1,0,1,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,1,1,-1,1,0,-1

%N a(n) = d(n) - (omega(n) * bigomega(n)), where d (number of divisors) = A000005, omega = A001221, bigomega = A001222.

%C a(n) = sigma_0(n) - omega(n) * nu(n), where sigma_0 = A000005, nu = A001221, omega = A001222. - The original name of the sequence.

%H Antti Karttunen, <a href="/A328958/b328958.txt">Table of n, a(n) for n = 1..20000</a>

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

%F a(n) = A000005(n) - A001222(n) * A001221(n) = A00005(n) - A113901(n).

%e a(144) = sigma_0(144) - omega(144) * nu(144) = 15 - 6 * 2 = 3.

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

%o (PARI) A328958(n) = (numdiv(n)-(omega(n)*bigomega(n))); \\ _Antti Karttunen_, Jan 27 2025

%Y Positions of first appearances are A328962.

%Y Zeros are A328956.

%Y Nonzeros are A328957.

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

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

%Y sigma_0(n) - 2 - (omega(n) - 1) * nu(n) is A328959(n).

%Y Cf. A000005, A001221, A001222, A112798, A124010, A323023, A328960, A328961, A328963, A328964.

%K sign

%O 1,72

%A _Gus Wiseman_, Nov 02 2019

%E More terms added and the function names in the definition replaced with standard OEIS ones - _Antti Karttunen_, Jan 27 2025