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

Author

Amiram Eldar, Oct 10 2023

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A000005, A001620, A007310, A366442.

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

Programs

Mathematica

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

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

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).