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 A289435 The arithmetic function v_3(n,3). 113
 1, 0, 2, 2, 3, 2, 4, 2, 5, 4, 6, 4, 7, 6, 8, 6, 9, 6, 10, 6, 11, 8, 12, 10, 13, 8, 14, 10, 15, 10, 16, 12, 17, 14, 18, 12, 19, 12, 20, 14, 21, 14, 22, 18, 23, 16, 24, 16, 25, 18, 26, 18, 27, 22, 28, 18, 29, 20, 30, 20, 31, 20, 32, 26, 33, 22, 34, 24, 35 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,3 REFERENCES J. Butterworth, Examining the arithmetic function v_g(n,h). Research Papers in Mathematics, B. Bajnok, ed., Gettysburg College, Vol. 8 (2008). LINKS Bela Bajnok, Additive Combinatorics: A Menu of Research Problems, arXiv:1705.07444 [math.NT], May 2017. See Table in Section 1.6.1. MAPLE a:= n-> n*max(seq((floor((d-1-igcd(d, 3))/3)+1)         /d, d=numtheory[divisors](n))): seq(a(n), n=2..100);  # Alois P. Heinz, Jul 07 2017 MATHEMATICA a[n_]:=n*Max[Table[(Floor[(d - 1 - GCD[d, 3])/3] + 1)/d, {d, Divisors[n]}]]; Table[a[n], {n, 2, 100}] (* Indranil Ghosh, Jul 08 2017 *) PROG (PARI) v(g, n, h)={my(t=0); fordiv(n, d, t=max(t, ((d-1-gcd(d, g))\h + 1)*(n/d))); t} a(n)=v(3, n, 3); \\ Andrew Howroyd, Jul 07 2017 (Python) from sympy import divisors, floor, gcd def a(n): return n*max([(floor((d - 1 - gcd(d, 3))/3) + 1)/d for d in divisors(n)]) print map(a, xrange(2, 101)) # Indranil Ghosh, Jul 08 2017 CROSSREFS Cf. A211316 (equals v_1(n,3)). Sequence in context: A117658 A325564 A323888 * A067540 A218701 A305790 Adjacent sequences:  A289432 A289433 A289434 * A289436 A289437 A289438 KEYWORD nonn AUTHOR N. J. A. Sloane, Jul 06 2017 EXTENSIONS a(41)-a(70) from Andrew Howroyd, Jul 07 2017 STATUS approved

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Last modified June 16 10:03 EDT 2019. Contains 324152 sequences. (Running on oeis4.)