A094520 Numbers such that all sums of two distinct divisors are not divisors.

1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 21, 22, 23, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 37, 38, 39, 41, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 55, 57, 58, 59, 61, 62, 63, 64, 65, 67, 68, 69, 71, 73, 74, 75, 76, 77, 79, 81, 82, 83, 85, 86, 87, 88, 89, 91

Offset: 1

Author

Reinhard Zumkeller, May 06 2004

Keywords

• nonn

Comments

The numbers of terms that do not exceed 10^k, for k = 1, 2, ..., are 9, 78, 770, 7683, 76799, 767791, 7677080, 76767834, 767667691, 7676629816, ... . Apparently, the asymptotic density of this sequence exists and equals 0.76766... . - Amiram Eldar, Apr 20 2025

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Sum-Free Set.

Crossrefs

Cf. A094518.

Complement of A094519.

Programs

Mathematica

aQ[n_] := AllTrue[Total /@ Subsets[Divisors[n], {2}], ! Divisible[n, #] &]; Select[Range[91], aQ] (* Amiram Eldar, Aug 31 2019 *)

PARI

isok(k) = {my(d = divisors(k)); for(i = 1, #d, for(j = 1, i-1, if(!(k % (d[i] + d[j])), return(0)))); 1;} \\ Amiram Eldar, Apr 20 2025

Formula

A094518(a(n)) = 0.