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A331828
Numbers k such that the divisors of k form an addition chain.
1
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
1,2
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.
EXAMPLE
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.
MAPLE
q:= n-> (s-> andmap(x-> x=1 or ormap(y-> y<x and
x-y in s, s), s))(numtheory[divisors](n)):
select(q, [$1..500])[]; # Alois P. Heinz, Jan 30 2020
PROG
(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
CROSSREFS
Subsequence of A308115.
Supersequence of A060765.
Sequence in context: A231565 A191743 A308115 * A377308 A258118 A177807
KEYWORD
nonn
AUTHOR
Zizheng Fang, Jan 27 2020
STATUS
approved