A239161 Numbers k such that the ratio (sum of divisors of k) /(sum of divisors d of k with d <= sqrt(k)) is an integer.

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, 33, 34, 35, 37, 38, 39, 41, 42, 43, 44, 46, 47, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 65, 66, 67, 68, 69, 71, 73, 74, 76, 77, 78, 79, 82, 83, 85, 86, 87, 88, 89

Offset: 1

Author

Michel Lagneau, Mar 11 2014

Keywords

• nonn

Comments

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

The corresponding integers are in A238502.

Includes all the primes and all the squarefree semiprimes (A006881). - Amiram Eldar, Nov 03 2024

Examples

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

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000203, A006881, A066839, A238502.

Programs

Mathematica

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

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