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A289436 The arithmetic function v_1(n,4).

%I A289436 #26 Apr 24 2020 09:43:04
%S A289436 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,
%T A289436 11,17,10,18,9,19,13,20,10,21,11,22,15,23,12,24,14,25,17,26,13,27,15,
%U A289436 28,19,29,15,30,15,31,21,32,16,33,17,34,23,35
%N A289436 The arithmetic function v_1(n,4).
%D A289436 J. Butterworth, Examining the arithmetic function v_g(n,h). Research Papers in Mathematics, B. Bajnok, ed., Gettysburg College, Vol. 8 (2008).
%H A289436 Bela Bajnok, <a href="https://arxiv.org/abs/1705.07444">Additive Combinatorics: A Menu of Research Problems</a>, arXiv:1705.07444 [math.NT], May 2017. See Table in Section 1.6.1.
%p A289436 a:= n-> n*max(seq((floor((d-2)/4)+1)/d, d=numtheory[divisors](n))):
%p A289436 seq(a(n), n=2..100);  # _Alois P. Heinz_, Jul 07 2017
%t A289436 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 *)
%o A289436 (PARI)
%o A289436 v(g,n,h)={my(t=0);fordiv(n,d,t=max(t,((d-1-gcd(d,g))\h + 1)*(n/d)));t}
%o A289436 a(n)=v(1,n,4); \\ _Andrew Howroyd_, Jul 07 2017
%o A289436 (Python)
%o A289436 from sympy import divisors, floor
%o A289436 def a(n): return int(n*max(int(floor((d - 2)/4) + 1)/d for d in divisors(n)))
%o A289436 print([a(n) for n in range(2, 101)]) # _Indranil Ghosh_, Jul 08 2017
%Y A289436 Cf. A289437, A289438.
%K A289436 nonn
%O A289436 2,3
%A A289436 _N. J. A. Sloane_, Jul 07 2017
%E A289436 a(41)-a(70) from _Andrew Howroyd_, Jul 07 2017