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A182084
a(n) = 3*n - n/p, where p is the smallest prime dividing n.
1
5, 8, 10, 14, 15, 20, 20, 24, 25, 32, 30, 38, 35, 40, 40, 50, 45, 56, 50, 56, 55, 68, 60, 70, 65, 72, 70, 86, 75, 92, 80, 88, 85, 98, 90, 110, 95, 104, 100, 122, 105, 128, 110, 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
OFFSET
2,1
COMMENTS
Conjectured to be minimal number of nodes in any non-bipartite regular graph of degree n, diameter 2 and girth 4.
(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
REFERENCES
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).
LINKS
FORMULA
a(n) = 3*n - A032742(n). - Amiram Eldar, May 27 2024
MATHEMATICA
a[n_] := (3 - 1/FactorInteger[n][[1, 1]]) * n; Array[a, 100, 2] (* Amiram Eldar, May 27 2024 *)
CROSSREFS
Sequence in context: A352676 A098594 A154315 * A262707 A257046 A314382
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Apr 11 2012
STATUS
approved