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

1,6

Links

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

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

Mathematica

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

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.

Sequence in context: A125072 A162642 A366246 * A355827 A139146 A340489

Adjacent sequences: A361202 A361203 A361204 * A361206 A361207 A361208

Keyword

sign,easy

Author

Gus Wiseman, Mar 16 2023

Status

approved