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
Robert Israel, Table of n, a(n) for n = 1..10000
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
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Aug 18 2022
STATUS
approved