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A331828 Numbers k such that the divisors of k form an addition chain.

%I A331828 #45 Jan 30 2020 07:39:26
%S A331828 1,2,4,6,8,12,16,18,20,24,30,32,36,40,42,48,54,60,64,72,80,84,90,96,
%T A331828 100,108,120,126,128,140,144,150,156,160,162,168,180,192,198,200,210,
%U A331828 216,220,240,252,256,264,270,272,280,288,294,300,312,320,324,330,336,342,360
%N A331828 Numbers k such that the divisors of k form an addition chain.
%C A331828 Every divisor of a term, except 1, can be expressed as the sum of two other divisors.
%C A331828 This sequence is a subsequence of A308115. Numbers that are in A308115 but not in this sequence include 462, 1300, 3234, etc.
%H A331828 Zizheng Fang, <a href="/A331828/b331828.txt">Table of n, a(n) for n = 1..10000</a>
%H A331828 Zizheng Fang, <a href="/A331828/a331828.txt">Python program to generate A331828</a>
%e A331828 1: divisors -- 1;
%e A331828 2: divisors -- 1, 2 = 1 + 1;
%e A331828 4: divisors -- 1, 2 = 1 + 1, 4 = 2 + 2;
%e A331828 6: divisors -- 1, 2 = 1 + 1, 3 = 1 + 2, 6 = 3 + 3;
%e A331828 8: divisors -- 1, 2 = 1 + 1, 4 = 2 + 2, 8 = 4 + 4;
%e A331828 12: divisors -- 1, 2 = 1 + 1, 3 = 1 + 2, 4 = 1 + 3, 6 = 2 + 4, 12 = 6 + 6.
%p A331828 q:= n-> (s-> andmap(x-> x=1 or ormap(y-> y<x and
%p A331828         x-y in s, s), s))(numtheory[divisors](n)):
%p A331828 select(q, [$1..500])[];  # _Alois P. Heinz_, Jan 30 2020
%o A331828 (PARI) isokd(k, d) = {for (j=1, k-1, if (vecsearch(d, d[k] - d[j]), return (1));); return (0);}
%o A331828 isok(k) = {my(d=divisors(k)); for (j=2, #d, if (! isokd(j, d), return(0));); return (1);} \\ _Michel Marcus_, Jan 30 2020
%Y A331828 Subsequence of A308115.
%Y A331828 Supersequence of A060765.
%K A331828 nonn
%O A331828 1,2
%A A331828 _Zizheng Fang_, Jan 27 2020