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%I #30 Aug 08 2023 03:22:18
%S 6,8,10,12,14,16,18,20,24,28,30,32,36,40,42,44,48,50,52,54,56,60,64,
%T 66,70,72,78,80,84,88,90,96,98,100,102,104,108,110,112,114,120,126,
%U 128,130,132,136,138,140,144,150,152,154,156,160,162,168,170,174,176,180,182,184,186,190
%N Numbers k that can be written as the sum of 6 divisors of k (not necessarily distinct).
%C Numbers divisible by at least one of 6, 8, 10, 14, 44, 52. For proof see link. - _Robert Israel_, Sep 02 2022
%C The asymptotic density of this sequence is 483/1430. - _Amiram Eldar_, Aug 08 2023
%H Robert Israel, <a href="/A356609/b356609.txt">Table of n, a(n) for n = 1..10000</a>
%H Robert Israel, <a href="/A356609/a356609.pdf">Proof that A356609 consists of all numbers divisible by at least one of 6, 8, 10, 14, 44, 52</a>.
%e 18 is in the sequence since 18 = 9+2+2+2+2+1, where each summand divides 18.
%p filter:= n-> ormap(t -> n mod t = 0, [6,8,10,14,44,52]):
%p select(filter, [$1..200]); # _Robert Israel_, Sep 02 2022
%t q[n_, k_] := AnyTrue[Tuples[Divisors[n], k], Total[#] == n &]; Select[Range[200], q[#, 6] &] (* _Amiram Eldar_, Aug 19 2022 *)
%o (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
%Y 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).
%K nonn
%O 1,1
%A _Wesley Ivan Hurt_, Aug 18 2022
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