|
| |
|
|
A051014
|
|
Nondividing sets on {1,2,...,n}.
|
|
3
| |
|
|
1, 2, 3, 5, 7, 11, 14, 21, 27, 38, 52, 73, 90, 123, 159, 211, 263, 344, 413, 535, 658, 832, 1026, 1276, 1499, 1846, 2226, 2708, 3229, 3912, 4592, 5541, 6495, 7795, 9207, 10908, 12547, 14852, 17358, 20493, 23709, 27744, 31921, 37250, 43013, 49936, 57319, 66318
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
COMMENTS
| A set is called nondividing if no element divides the sum of any nonempty subset of the other elements.
|
|
|
LINKS
| Eric Weisstein's World of Mathematics, Nondividing Set
|
|
|
EXAMPLE
| a(5) = 11 because there are 11 nondividing subsets of {1,2,3,4,5}: {}, {1}, {2}, {3}, {4}, {5}, {2,3}, {2,5}, {3,4}, {3,5}, {4,5}.
a(7) = 21: {}, {1}, {2}, {3}, {4}, {5}, {6}, {7}, {2,3}, {2,5}, {2,7}, {3,4}, {3,5}, {3,7}, {4,5}, {4,6}, {4,7}, {5,6}, {5,7}, {6,7}, {4,6,7}.
|
|
|
MAPLE
| sums:= proc(s) option remember;
local i, m;
m:= max(s[]);
`if` (m<1, {}, {m, seq([i, i+m][], i=sums(s minus {m}))})
end:
b:= proc(i, s) option remember;
local j, ok, t, si;
if i<2 then 1
else si:= s union {i};
ok:= true;
for j in sums(si) while ok do
for t in si while ok do
if irem(j, t)=0 and t<>j then ok:= false fi
od
od;
b(i-1, s) +`if`(ok, b(i-1, si), 0)
fi
end:
a:= n-> `if` (n=0, 1, 1+b (n, {})):
seq (a(n), n=0..25); # Alois P. Heinz, Mar 08 2011
|
|
|
CROSSREFS
| Row sums of A187489. Cf. A068063.
Sequence in context: A051056 A055803 A023027 * A035968 A112581 A035976
Adjacent sequences: A051011 A051012 A051013 * A051015 A051016 A051017
|
|
|
KEYWORD
| nonn,nice
|
|
|
AUTHOR
| Eric Weisstein (eric(AT)weisstein.com)
|
|
|
EXTENSIONS
| More terms from David Wasserman (wasserma(AT)spawar.navy.mil), Feb 15 2002
a(41)-a(47) from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Mar 08 2011
|
| |
|
|
