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

1,1

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

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.

Example

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

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 *)

Prog

(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

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).

Sequence in context: A060652 A020739 A064466 * A026286 A187085 A303580

Adjacent sequences: A356606 A356607 A356608 * A356610 A356611 A356612

Keyword

nonn

Author

Wesley Ivan Hurt, Aug 18 2022

Status

approved