A239161 - OEIS

%I #15 Nov 03 2024 09:35:24

%S 1,2,3,5,6,7,8,10,11,13,14,15,17,19,20,21,22,23,24,26,27,28,29,31,32,

%T 33,34,35,37,38,39,41,42,43,44,46,47,51,52,53,54,55,57,58,59,60,61,62,

%U 65,66,67,68,69,71,73,74,76,77,78,79,82,83,85,86,87,88,89

%N Numbers k such that the ratio (sum of divisors of k) /(sum of divisors d of k with d <= sqrt(k)) is an integer.

%C Numbers k such that A000203(k)/A066839(k) is an integer.

%C The corresponding integers are in A238502.

%C Includes all the primes and all the squarefree semiprimes (A006881). - _Amiram Eldar_, Nov 03 2024

%H Vincenzo Librandi, <a href="/A239161/b239161.txt">Table of n, a(n) for n = 1..1000</a>

%e 13 is in the sequence because A000203(13)/A066839(13) = 14/1 = 14 is an integer.

%t lst={}; f[n_]:=DivisorSigma[1,n]/Plus@@Select[Divisors@n,#<=Sqrt@n&];Do[If[IntegerQ[f[n]],AppendTo[lst, n]],{n,1,200}];lst

%o (PARI) is(k) = if(k == 1, 1, my(f = factor(k)); !(sigma(f) % sumdiv(f, d, d * (d^2 <= k)))); \\ _Amiram Eldar_, Nov 03 2024

%Y Cf. A000203, A006881, A066839, A238502.

%K nonn

%O 1,2

%A _Michel Lagneau_, Mar 11 2014