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A356609
Numbers k that can be written as the sum of 6 divisors of k (not necessarily distinct).
10
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
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
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Aug 18 2022
STATUS
approved