A355140 - OEIS

%I #12 Dec 22 2022 13:18:03

%S 1,1,2,1,3,2,4,2,3,3,6,2,7,4,4,3,9,3,10,3,5,6,12,3,8,7,7,5,15,4,16,5,

%T 8,9,9,4,19,10,10,5,21,5,22,7,8,12,24,5,16,8,13,9,27,7,14,7,14,15,30,

%U 5,31,16,11,9,16,8,34,11,17,9,36,6,37,19,13,13,19

%N n/d(n) rounded to the nearest integer, where d(n) is the number of divisors of n (A000005).

%C In the ambiguous case, fractions are rounded up.

%F a(n) = round (n / A000005(n)).

%e a(1) = round (1 / 1) = 1;

%e a(4) = round (4 / 3) = 1;

%e a(5) = round (5 / 2) = 3;

%t Table[Floor[n/DivisorSigma[0,n]+1/2],{n,100}] (* _Harvey P. Dale_, Dec 22 2022 *)

%o (Python)

%o from sympy import divisor_count

%o def A355140(n): return (2*n+(d:=divisor_count(n)))//(2*d) # _Chai Wah Wu_, Jun 20 2022

%Y Cf. A000005, A078709 (floor), A334762 (ceiling), A090395 (numerators), A090387 (denominators).

%K nonn

%O 1,3

%A _Sameer Khan_, Jun 20 2022