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A366441
The number of divisors of the 5-rough numbers (A007310).
2
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
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
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Oct 10 2023
STATUS
approved