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A356635
Numbers k that can be written as the sum of 7 divisors of k (not necessarily distinct).
9
7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 27, 28, 30, 32, 33, 35, 36, 39, 40, 42, 44, 45, 48, 49, 50, 52, 54, 55, 56, 60, 63, 64, 66, 68, 70, 72, 75, 77, 78, 80, 81, 84, 88, 90, 91, 96, 98, 99, 100, 102, 104, 105, 108, 110, 112, 114, 117, 119, 120, 126, 128, 130
OFFSET
1,1
COMMENTS
If k is in the sequence then so is k*m for positive m. - David A. Corneth, Aug 19 2022
Numbers that are divisible by at least one of 7, 8, 9, 10, 12, 15, 22, 33, 39, 52, 55, 68, 102, 114, 138. For proof, see link. - Robert Israel, Sep 02 2022
The asymptotic density of this sequence is 17819629/37182145 = 0.479252... . - Amiram Eldar, Aug 08 2023
EXAMPLE
10 is in the sequence since 10 = 2+2+2+1+1+1+1, where each summand divides 10.
MAPLE
filter:= n -> ormap(t -> n mod t = 0, [7, 8, 9, 10, 12, 15, 22, 33, 39, 52, 55, 68, 102, 114, 138]):
select(filter, [$1..200]); # Robert Israel, Sep 02 2022
MATHEMATICA
q[n_, k_] := AnyTrue[Tuples[Divisors[n], k], Total[#] == n &]; Select[Range[130], q[#, 7] &] (* 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)), , [7, 7]); \\ 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), A356609 (j=6), this sequence (j=7), A356657 (j=8), A356659 (j=9), A356660 (j=10).
Sequence in context: A065976 A236683 A120200 * A343297 A106108 A120309
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Aug 18 2022
STATUS
approved