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A355641 Numbers k that can be written as the sum of 5 divisors of k (not necessarily distinct). 10
5, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 25, 27, 28, 30, 32, 35, 36, 40, 42, 45, 48, 50, 54, 55, 56, 60, 63, 64, 65, 66, 70, 72, 75, 78, 80, 81, 84, 85, 88, 90, 95, 96, 98, 99, 100, 102, 104, 105, 108, 110, 112, 114, 115, 117, 120, 125, 126, 128, 130, 132, 135, 136, 138 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Numbers that are divisible by at least one of 5, 6, 8, 9, 14 and 21. For proof see link. - Robert Israel, Sep 01 2022
The asymptotic density of this sequence is 17/35. - Amiram Eldar, Aug 08 2023
LINKS
EXAMPLE
9 is in the sequence since 9 = 3+3+1+1+1, where each summand divides 9.
MAPLE
F:= proc(x, S, j) option remember;
local s, k;
if j = 0 then return(x = 0) fi;
if S = [] or x > j*S[-1] or x < j*S[1] then return false fi;
s:= S[-1];
for k from 0 to min(j, floor(x/s)) do
if procname(x-k*s, S[1..-2], j-k) then return true fi
od;
false
end proc:
select(t -> F(t, sort(convert(numtheory:-divisors(t), list)), 5), [$1..200]); # Robert Israel, Aug 31 2022
MATHEMATICA
q[n_, k_] := AnyTrue[Tuples[Divisors[n], k], Total[#] == n &]; Select[Range[140], q[#, 5] &] (* 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)), , [5, 5]); \\ 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), this sequence (j=5), A356609 (j=6), A356635 (j=7), A356657 (j=8), A356659 (j=9), A356660 (j=10).
Sequence in context: A296562 A057854 A033266 * A363701 A353193 A102408
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Aug 18 2022
STATUS
approved

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Last modified March 28 11:46 EDT 2024. Contains 371241 sequences. (Running on oeis4.)