A345219 Number of divisors of n with an odd number of primes not exceeding them.

0, 1, 0, 1, 1, 2, 0, 1, 0, 2, 1, 3, 0, 1, 1, 1, 1, 3, 0, 2, 0, 2, 1, 4, 2, 2, 1, 2, 0, 3, 1, 2, 2, 3, 2, 5, 0, 1, 0, 2, 1, 3, 0, 2, 1, 2, 1, 5, 1, 4, 2, 3, 0, 4, 2, 2, 0, 1, 1, 5, 0, 2, 0, 2, 1, 4, 1, 4, 2, 4, 0, 6, 1, 2, 3, 2, 2, 4, 0, 2, 1, 2, 1, 6, 3, 2, 1, 3, 0, 4, 0, 2, 1

Offset

1,6

Links

Table of n, a(n) for n=1..93.

Formula

a(n) = Sum_{d|n} (pi(d) mod 2).

Example

a(24) = 4; The divisors d of 24 are: 1, 2, 3, 4, 6, 8, 12, 24 and the corresponding values of pi(d) are: 0, 1, 2, 2, 3, 4, 5, 9. There are 4 odd values of pi(d).

Mathematica

Table[Sum[Mod[PrimePi[k], 2] (1 - Ceiling[n/k] + Floor[n/k]), {k, n}], {n, 100}]

Prog

(PARI) a(n) = sumdiv(n, d, primepi(d) % 2); \\ Michel Marcus, Jun 11 2021

Crossrefs

Cf. A000005, A000720, A345220.

Sequence in context: A117054 A036579 A139353 * A357705 A363945 A029397

Adjacent sequences: A345216 A345217 A345218 * A345220 A345221 A345222

Keyword

nonn

Author

Wesley Ivan Hurt, Jun 11 2021

Status

approved