

A211316


Maximal size of sumfree 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
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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 nonisomorphic sumfree sets, in Proc. First Australian Conf. Combinatorial Math., Univ. Newcastle, 1972, pp. 141143.


LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 2..10000
Bela Bajnok, Additive Combinatorics: A Menu of Research Problems, arXiv:1705.07444 [math.NT], May 2017. See Table in Section 1.6.1.
Ben Green and Imre Z. Ruzsa, Sumfree sets in abelian groups, arXiv:math/0307142 [math.CO], 2004.


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) = (n1)/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, n1, n]/3]
Table[a[n], {n, 2, 100}] (* JeanFrançois Alcover, Aug 02 2018, from PARI *)


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
 Reinhard Zumkeller, Apr 25 2012
(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, n1, n)/3 \\ Charles R Greathouse IV, Sep 02 2015


CROSSREFS

Bisection: A211317. Cf. A007865, A027748, A003627.
Sequence in context: A178804 A322355 A242112 * A280226 A307995 A061889
Adjacent sequences: A211313 A211314 A211315 * A211317 A211318 A211319


KEYWORD

nonn


AUTHOR

N. J. A. Sloane, Apr 24 2012


STATUS

approved



