A140237 - OEIS

%I #14 Oct 24 2023 02:16:18

%S 1,5,7,8,16,17,19,20,23,25,37,41,42,43,47,49,64,65,67,68,69,70,71,73,

%T 74,77,79,101,103,107,108,109,113,149,150,151,155,157,163,164,165,166,

%U 167,169,197,199,211,223,257,259,263,264,265,267,268,269,271,274,275,277

%N A number n is included if (Sum_{k=1..n} d(k)) is divisible by d(n), where d(n) is the number of positive divisors of n.

%C sum{k=1 to n} d(k) = sum{k=1 to n} floor(n/k) = A006218(n).

%H Michael De Vlieger, <a href="/A140237/b140237.txt">Table of n, a(n) for n = 1..10000</a>

%t s = 0; Reap[Do[If[Divisible[s += #, #], Sow[i]] &[DivisorSigma[0, i]], {i, 280}] ][[-1, 1]] (* _Michael De Vlieger_, Oct 23 2023 *)

%o (Python)

%o from math import isqrt

%o from sympy import divisor_count

%o def A140237_gen(startvalue=1): # generator of terms >= startvalue

%o     return filter(lambda n: not (-(s:=isqrt(n))**2+(sum(n//k for k in range(1,s+1))<<1))%divisor_count(n),count(max(startvalue,1)))

%o A140237_list = list(islice(A140237_gen(),30)) # _Chai Wah Wu_, Oct 23 2023

%Y Cf. A000005, A006218, A140238.

%K nonn

%O 1,2

%A _Leroy Quet_, May 14 2008

%E Extended by _Ray Chandler_, Jun 25 2009