A356609 Numbers k that can be written as the sum of 6 divisors of k (not necessarily distinct).

6, 8, 10, 12, 14, 16, 18, 20, 24, 28, 30, 32, 36, 40, 42, 44, 48, 50, 52, 54, 56, 60, 64, 66, 70, 72, 78, 80, 84, 88, 90, 96, 98, 100, 102, 104, 108, 110, 112, 114, 120, 126, 128, 130, 132, 136, 138, 140, 144, 150, 152, 154, 156, 160, 162, 168, 170, 174, 176, 180, 182, 184, 186, 190

Offset: 1

Author

Wesley Ivan Hurt, Aug 18 2022

Keywords

• nonn

Comments

Numbers divisible by at least one of 6, 8, 10, 14, 44, 52. For proof see link. - Robert Israel, Sep 02 2022

The asymptotic density of this sequence is 483/1430. - Amiram Eldar, Aug 08 2023

Examples

			18 is in the sequence since 18 = 9+2+2+2+2+1, where each summand divides 18.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Robert Israel, Proof that A356609 consists of all numbers divisible by at least one of 6, 8, 10, 14, 44, 52.

Crossrefs

Numbers k that can be written as the sum of j divisors of k (not necessarily distinct) for j=1..10: A000027 (j=1), A299174 (j=2), A355200 (j=3), A354591 (j=4), A355641 (j=5), this sequence (j=6), A356635 (j=7), A356657 (j=8), A356659 (j=9), A356660 (j=10).

Programs

Maple

filter:= n-> ormap(t -> n mod t = 0, [6,8,10,14,44,52]):
select(filter, [$1..200]); # Robert Israel, Sep 02 2022

Mathematica

q[n_, k_] := AnyTrue[Tuples[Divisors[n], k], Total[#] == n &]; Select[Range[200], q[#, 6] &] (* Amiram Eldar, Aug 19 2022 *)

PARI

isok(k) = my(d=divisors(k)); forpart(p=k, if (setintersect(d, Set(p)) == Set(p), return(1)), , [6,6]); \\ Michel Marcus, Aug 19 2022