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 A289436 The arithmetic function v_1(n,4). 113
 1, 1, 2, 1, 3, 2, 4, 3, 5, 3, 6, 3, 7, 5, 8, 4, 9, 5, 10, 7, 11, 6, 12, 6, 13, 9, 14, 7, 15, 8, 16, 11, 17, 10, 18, 9, 19, 13, 20, 10, 21, 11, 22, 15, 23, 12, 24, 14, 25, 17, 26, 13, 27, 15, 28, 19, 29, 15, 30, 15, 31, 21, 32, 16, 33, 17, 34, 23, 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-2)/4)+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 - 2)/4] + 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(1, n, 4); \\ Andrew Howroyd, Jul 07 2017 (Python) from sympy import divisors, floor def a(n): return n*max([(floor((d - 2)/4) + 1)/d for d in divisors(n)]) print map(a, xrange(2, 101)) # Indranil Ghosh, Jul 08 2017 CROSSREFS Cf. A289437, A289438. Sequence in context: A257909 A289439 A213633 * A282745 A097140 A028242 Adjacent sequences:  A289433 A289434 A289435 * A289437 A289438 A289439 KEYWORD nonn AUTHOR N. J. A. Sloane, Jul 07 2017 EXTENSIONS a(41)-a(70) from Andrew Howroyd, Jul 07 2017 STATUS approved

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Last modified June 25 10:10 EDT 2019. Contains 324351 sequences. (Running on oeis4.)