cp's OEIS Frontend

A355140 n/d(n) rounded to the nearest integer, where d(n) is the number of divisors of n (A000005).

%I A355140 #12 Dec 22 2022 13:18:03
%S A355140 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 A355140 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 A355140 5,31,16,11,9,16,8,34,11,17,9,36,6,37,19,13,13,19
%N A355140 n/d(n) rounded to the nearest integer, where d(n) is the number of divisors of n (A000005).
%C A355140 In the ambiguous case, fractions are rounded up.
%F A355140 a(n) = round (n / A000005(n)).
%e A355140 a(1) = round (1 / 1) = 1;
%e A355140 a(4) = round (4 / 3) = 1;
%e A355140 a(5) = round (5 / 2) = 3;
%t A355140 Table[Floor[n/DivisorSigma[0,n]+1/2],{n,100}] (* _Harvey P. Dale_, Dec 22 2022 *)
%o A355140 (Python)
%o A355140 from sympy import divisor_count
%o A355140 def A355140(n): return (2*n+(d:=divisor_count(n)))//(2*d) # _Chai Wah Wu_, Jun 20 2022
%Y A355140 Cf. A000005, A078709 (floor), A334762 (ceiling), A090395 (numerators), A090387 (denominators).
%K A355140 nonn
%O A355140 1,3
%A A355140 _Sameer Khan_, Jun 20 2022