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A356635
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Numbers k that can be written as the sum of 7 divisors of k (not necessarily distinct).
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9
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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
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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Robert Israel, Proof that A356635 consists of all numbers divisible by at least one of 7, 8, 9, 10, 12, 15, 22, 33, 39, 52, 55, 68, 102, 114, 138.
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EXAMPLE
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10 is in the sequence since 10 = 2+2+2+1+1+1+1, where each summand divides 10.
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MAPLE
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filter:= n -> ormap(t -> n mod t = 0, [7, 8, 9, 10, 12, 15, 22, 33, 39, 52, 55, 68, 102, 114, 138]):
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MATHEMATICA
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q[n_, k_] := AnyTrue[Tuples[Divisors[n], k], Total[#] == n &]; Select[Range[130], q[#, 7] &] (* Amiram Eldar, Aug 19 2022 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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