login
Numbers k such that the divisors of k form an addition chain.
1

%I #45 Jan 30 2020 07:39:26

%S 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 100,108,120,126,128,140,144,150,156,160,162,168,180,192,198,200,210,

%U 216,220,240,252,256,264,270,272,280,288,294,300,312,320,324,330,336,342,360

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

%C Every divisor of a term, except 1, can be expressed as the sum of two other divisors.

%C This sequence is a subsequence of A308115. Numbers that are in A308115 but not in this sequence include 462, 1300, 3234, etc.

%H Zizheng Fang, <a href="/A331828/b331828.txt">Table of n, a(n) for n = 1..10000</a>

%H Zizheng Fang, <a href="/A331828/a331828.txt">Python program to generate A331828</a>

%e 1: divisors -- 1;

%e 2: divisors -- 1, 2 = 1 + 1;

%e 4: divisors -- 1, 2 = 1 + 1, 4 = 2 + 2;

%e 6: divisors -- 1, 2 = 1 + 1, 3 = 1 + 2, 6 = 3 + 3;

%e 8: divisors -- 1, 2 = 1 + 1, 4 = 2 + 2, 8 = 4 + 4;

%e 12: divisors -- 1, 2 = 1 + 1, 3 = 1 + 2, 4 = 1 + 3, 6 = 2 + 4, 12 = 6 + 6.

%p q:= n-> (s-> andmap(x-> x=1 or ormap(y-> y<x and

%p x-y in s, s), s))(numtheory[divisors](n)):

%p select(q, [$1..500])[]; # _Alois P. Heinz_, Jan 30 2020

%o (PARI) isokd(k, d) = {for (j=1, k-1, if (vecsearch(d, d[k] - d[j]), return (1));); return (0);}

%o isok(k) = {my(d=divisors(k)); for (j=2, #d, if (! isokd(j, d), return(0));); return (1);} \\ _Michel Marcus_, Jan 30 2020

%Y Subsequence of A308115.

%Y Supersequence of A060765.

%K nonn

%O 1,2

%A _Zizheng Fang_, Jan 27 2020