|
|
A211316
|
|
Maximal size of sum-free set in additive group of integers mod n.
|
|
5
|
|
|
1, 1, 2, 2, 3, 2, 4, 3, 5, 4, 6, 4, 7, 6, 8, 6, 9, 6, 10, 7, 11, 8, 12, 10, 13, 9, 14, 10, 15, 10, 16, 12, 17, 14, 18, 12, 19, 13, 20, 14, 21, 14, 22, 18, 23, 16, 24, 16, 25, 18, 26, 18, 27, 22, 28, 19, 29, 20, 30, 20, 31, 21, 32, 26, 33, 22, 34, 24, 35, 24
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
2,3
|
|
REFERENCES
|
Bela Bajnok, Additive Combinatorics: A Menu of Research Problems, Manuscript, May 2017. See Table in Section 1.6.1.
A. P. Street, Counting non-isomorphic sum-free sets, in Proc. First Australian Conf. Combinatorial Math., Univ. Newcastle, 1972, pp. 141-143.
|
|
LINKS
|
|
|
FORMULA
|
If n is divisible by a prime == 2 mod 3 then a(n) = n(p+1)/(3p) where p is the smallest such prime divisor; otherwise if n is divisible by 3 then a(n) = n/3; otherwise all prime divisors of n are == 1 mod 3 and a(n) = (n-1)/3.
In particular, a(2n) = n (cf. A211317).
|
|
MATHEMATICA
|
a[n_] := Module[{f = FactorInteger[n][[All, 1]]}, For[i = 1, i <= Length[f], i++, If[Mod[f[[i]], 3]==2, Return[n*(f[[i]] + 1)/3/f[[i]]]]]; If[Mod[n, 3] == 1, n-1, n]/3]
|
|
PROG
|
(Haskell)
a211316 n | not $ null ps = n * (head ps + 1) `div` (3 * head ps)
| m == 0 = n'
| otherwise = (n - 1) `div` 3
where ps = [p | p <- a027748_row n, mod p 3 == 2]
(n', m) = divMod n 3
(PARI) a(n)=my(f=factor(n)[, 1]); for(i=1, #f, if(f[i]%3==2, return(n*(f[i]+1)/3/f[i]))); if(n%3, n-1, n)/3 \\ Charles R Greathouse IV, Sep 02 2015
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|