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

1, 2, 4, 6, 8, 12, 16, 18, 20, 24, 30, 32, 36, 40, 42, 48, 54, 60, 64, 72, 80, 84, 90, 96, 100, 108, 120, 126, 128, 140, 144, 150, 156, 160, 162, 168, 180, 192, 198, 200, 210, 216, 220, 240, 252, 256, 264, 270, 272, 280, 288, 294, 300, 312, 320, 324, 330, 336, 342, 360

Offset: 1

Author

Zizheng Fang, Jan 27 2020

Keywords

• nonn

Comments

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

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

Examples

			1: divisors -- 1;
2: divisors -- 1, 2 = 1 + 1;
4: divisors -- 1, 2 = 1 + 1, 4 = 2 + 2;
6: divisors -- 1, 2 = 1 + 1, 3 = 1 + 2, 6 = 3 + 3;
8: divisors -- 1, 2 = 1 + 1, 4 = 2 + 2, 8 = 4 + 4;
12: divisors -- 1, 2 = 1 + 1, 3 = 1 + 2, 4 = 1 + 3, 6 = 2 + 4, 12 = 6 + 6.
		

Links

• Zizheng Fang, Table of n, a(n) for n = 1..10000
• Zizheng Fang, Python program to generate A331828

Crossrefs

Subsequence of A308115.

Supersequence of A060765.

Programs

Maple

q:= n-> (s-> andmap(x-> x=1 or ormap(y-> yAlois P. Heinz, Jan 30 2020

PARI

isokd(k, d) = {for (j=1, k-1, if (vecsearch(d, d[k] - d[j]), return (1));); return (0);}
isok(k) = {my(d=divisors(k)); for (j=2, #d, if (! isokd(j, d), return(0));); return (1);} \\ Michel Marcus, Jan 30 2020