A366441 The number of divisors of the 5-rough numbers (A007310).

1, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 4, 2, 2, 2, 2, 3, 2, 4, 2, 2, 4, 2, 2, 2, 4, 2, 2, 4, 2, 4, 4, 2, 2, 2, 2, 2, 2, 4, 4, 3, 4, 2, 2, 4, 2, 2, 4, 4, 2, 2, 4, 2, 4, 2, 2, 3, 2, 6, 2, 2, 4, 4, 2, 2, 2, 2, 4, 4, 4, 2, 4, 4, 4, 2, 2, 2, 2, 4, 2, 2, 6, 4, 2, 4, 2, 4

Offset

1,2

Links

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

Formula

a(n) = A000005(A007310(n)).

Sum_{k=1..n} a(k) ~ (log(n) + 2*gamma - 1 + 2*log(6)) * n / 3, where gamma is Euler's constant (A001620).

Mathematica

a[n_] := DivisorSigma[0, 2*Floor[3*n/2] - 1]; Array[a, 100]

Prog

(PARI) a(n) = numdiv((3*n)\2 << 1 - 1)
(Python)
from sympy import divisor_count
def A366441(n): return divisor_count((n+(n>>1)<<1)-1) # Chai Wah Wu, Oct 10 2023

Crossrefs

Cf. A000005, A001620, A007310, A366442.

Similar sequences: A048691, A072048, A076400, A099774, A358040, A363194, A363195.

Sequence in context: A147793 A352201 A052298 * A179938 A081412 A082863

Adjacent sequences: A366438 A366439 A366440 * A366442 A366443 A366444

Keyword

nonn,easy

Author

Amiram Eldar, Oct 10 2023

Status

approved