Zizheng Fang has authored 3 sequences.
A334354
The number of optimal sets of n distinct integers less than or equal to k with this property: the sum of every two members of this set divides the product of all the members of this set. An optimal set with this property is one whose greatest member is the least possible.
Original entry on oeis.org
1, 1, 1, 1, 1, 1, 3, 1, 2, 6, 1, 2, 5, 4, 1, 1, 1, 196, 115, 34, 4, 674, 303, 86, 14, 1, 852, 164, 19, 1, 1, 176, 19, 1, 1, 44503, 11396
Offset: 1
n=1:
1
n=2:
3, 6
3*6 = 18
3+6 divides 18
n=3:
3, 12, 15
3*12*15 = 540
3+12 divides 540
3+15 divides 540
12+15 divides 540
n=4:
2, 6, 10, 14
2*6*10*14 = 1680
2+6 divides 1680
2+10 divides 1680
2+14 divides 1680
6+10 divides 1680
6+14 divides 1680
10+14 divides 1680
n=5:
2, 6, 10, 14, 18
n=6:
2, 6, 10, 14, 18, 22
n=7:
2, 4, 10, 14, 18, 22, 26
2, 6, 10, 14, 18, 22, 26
4, 6, 10, 14, 18, 22, 26
n=8:
2, 4, 6, 10, 14, 18, 22, 26
n=9:
2, 6, 8, 10, 14, 18, 22, 26, 34
2, 6, 10, 14, 18, 22, 26, 30, 34
A334352
The least positive integer k such that there exists a set of n distinct integers less than or equal to k with this property: the sum of every two members of this set divides the product of all the members of this set.
Original entry on oeis.org
1, 6, 15, 14, 18, 22, 26, 26, 34, 38, 38, 29, 29, 29, 29, 37, 41, 43, 43, 43, 43, 47, 47, 47, 47, 47, 59, 59, 59, 59, 61, 71, 71, 71, 77, 79, 79
Offset: 1
n=1:
1
n=2:
3, 6
3*6 = 18
3+6 divides 18
n=3:
3, 12, 15
3*12*15 = 540
3+12 divides 540
3+15 divides 540
12+15 divides 540
n=4:
2, 6, 10, 14
2*6*10*14 = 1680
2+6 divides 1680
2+10 divides 1680
2+14 divides 1680
6+10 divides 1680
6+14 divides 1680
10+14 divides 1680
n=5:
2, 6, 10, 14, 18
n=6:
2, 6, 10, 14, 18, 22
n=7:
2, 4, 10, 14, 18, 22, 26
2, 6, 10, 14, 18, 22, 26
4, 6, 10, 14, 18, 22, 26
n=8:
2, 4, 6, 10, 14, 18, 22, 26
n=9:
2, 6, 8, 10, 14, 18, 22, 26, 34
2, 6, 10, 14, 18, 22, 26, 30, 34
A331828
Numbers k such that the divisors of k form an addition chain.
Original entry on oeis.org
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
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.
-
q:= n-> (s-> andmap(x-> x=1 or ormap(y-> yAlois P. Heinz, Jan 30 2020
-
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
Comments