A361205 a(n) = 2*omega(n) - bigomega(n).

0, 1, 1, 0, 1, 2, 1, -1, 0, 2, 1, 1, 1, 2, 2, -2, 1, 1, 1, 1, 2, 2, 1, 0, 0, 2, -1, 1, 1, 3, 1, -3, 2, 2, 2, 0, 1, 2, 2, 0, 1, 3, 1, 1, 1, 2, 1, -1, 0, 1, 2, 1, 1, 0, 2, 0, 2, 2, 1, 2, 1, 2, 1, -4, 2, 3, 1, 1, 2, 3, 1, -1, 1, 2, 1, 1, 2, 3, 1, -1, -2, 2, 1, 2

Offset: 1

Author

Gus Wiseman, Mar 16 2023

Keywords

• sign
• easy

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Without doubling omega we have -A046660.

Positions of 0's are A067801, counted by A239959.

Positions of negative terms are A360558, counted by A360254.

Positions of nonpositive terms are A361204, counted by A237363.

Positions of positive terms are A361393, counted by A237365.

Positions of nonnegative terms are A361395, counted by A361394.

A001221 (omega) counts distinct prime factors.

A001222 (bigomega) counts prime factors.

A112798 lists prime indices, sum A056239.

Cf. A061395, A067340, A111907, A324517, A324522, A326567/A326568.

Cf. A077761, A083342, A136141.

Programs

Mathematica

Table[2*PrimeNu[n]-PrimeOmega[n],{n,100}]

Formula

Additive with a(p^e) = 2 - e. - Amiram Eldar, Mar 26 2023

Sum_{k=1..n} a(k) = n * log(log(n)) + c * n + O(n/log(n)), where c = 2*A077761 - A083342 = A077761 - A136141 = -0.511659... . - Amiram Eldar, Oct 01 2023