A366441 - OEIS

%I #12 Oct 10 2023 16:25:34

%S 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,

%T 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,

%U 4,4,2,4,4,4,2,2,2,2,4,2,2,6,4,2,4,2,4

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

%H Amiram Eldar, <a href="/A366441/b366441.txt">Table of n, a(n) for n = 1..10000</a>

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

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

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

%o (PARI) a(n) = numdiv((3*n)\2 << 1 - 1)

%o (Python)

%o from sympy import divisor_count

%o def A366441(n): return divisor_count((n+(n>>1)<<1)-1) # _Chai Wah Wu_, Oct 10 2023

%Y Cf. A000005, A001620, A007310, A366442.

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

%K nonn,easy

%O 1,2

%A _Amiram Eldar_, Oct 10 2023