A351519 a(n) = tau(n) + pi(n) - omega(n).

1, 2, 3, 4, 4, 5, 5, 7, 6, 6, 6, 9, 7, 8, 8, 10, 8, 11, 9, 12, 10, 10, 10, 15, 11, 11, 12, 13, 11, 15, 12, 16, 13, 13, 13, 18, 13, 14, 14, 18, 14, 18, 15, 18, 18, 16, 16, 23, 17, 19, 17, 19, 17, 22, 18, 22, 18, 18, 18, 26, 19, 20, 22, 24, 20, 23, 20, 23, 21, 24, 21, 30, 22, 23, 25, 25

Offset: 1

Author

Wesley Ivan Hurt, Feb 12 2022

Keywords

• nonn

Comments

Number of numbers <= n that are either prime, a divisor of n, or both.

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005 (tau), A000720 (pi), A001221 (omega).

Programs

Maple

map(numtheory:-tau + numtheory:-pi - nops @ numtheory:-factorset, [$1..100]);
# Robert Israel, Dec 09 2024

Mathematica

Table[DivisorSigma[0, n] + PrimePi[n] - PrimeNu[n], {n, 100}]

Formula

a(n) = A000005(n) + A000720(n) - A001221(n).