A182084 - OEIS

%I #18 May 27 2024 02:37:46

%S 5,8,10,14,15,20,20,24,25,32,30,38,35,40,40,50,45,56,50,56,55,68,60,

%T 70,65,72,70,86,75,92,80,88,85,98,90,110,95,104,100,122,105,128,110,

%U 120,115,140,120,140,125,136,130,158,135,154,140,152,145,176,150,182,155,168,160,182,165,200,170,184,175,212,180,218,185,200,190,220,195,236,200

%N a(n) = 3*n - n/p, where p is the smallest prime dividing n.

%C Conjectured to be minimal number of nodes in any non-bipartite regular graph of degree n, diameter 2 and girth 4.

%C (5/2)*n <= a(n) <= 3*n-1, the lower limit corresponds to even n's, the upper limit to odd prime n's. - _Zak Seidov_, Apr 13 2012

%D J. Sheehan, An extremal problem in finite graph theory, in: Infinite and finite sets (Colloq., Keszthely, 1973; dedicated to P. Erdős on his 60th birthday), Vol. III, pp. 1235-1239. Colloq. Math. Soc. Janos Bolyai, Vol. 10, North-Holland, Amsterdam, 1975. MR0376429 (51 #12604).

%H Amiram Eldar, <a href="/A182084/b182084.txt">Table of n, a(n) for n = 2..10000</a>

%F a(n) = 3*n - A032742(n). - _Amiram Eldar_, May 27 2024

%t a[n_] := (3 - 1/FactorInteger[n][[1, 1]]) * n; Array[a, 100, 2] (* _Amiram Eldar_, May 27 2024 *)

%Y Cf. A020639, A032742.

%K nonn

%O 2,1

%A _N. J. A. Sloane_, Apr 11 2012