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A289440 The arithmetic function v_3(n,5).

%I A289440 #19 Apr 23 2020 10:56:56
%S A289440 1,0,2,1,3,2,4,2,5,2,6,3,7,3,8,4,9,4,10,6,11,5,12,5,13,6,14,6,15,6,16,
%T A289440 6,17,10,18,8,19,9,20,8,21,9,22,10,23,10,24,14,25,12,26,11,27,11,28,
%U A289440 12,29,12,30,12,31,18,32,15,33,14,34,15,35
%N A289440 The arithmetic function v_3(n,5).
%D A289440 J. Butterworth, Examining the arithmetic function v_g(n,h). Research Papers in Mathematics, B. Bajnok, ed., Gettysburg College, Vol. 8 (2008).
%H A289440 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 A289440 a:= n-> n*max(seq((floor((d-1-igcd(d, 3))/5)+1)
%p A289440         /d, d=numtheory[divisors](n))):
%p A289440 seq(a(n), n=2..100);  # _Alois P. Heinz_, Jul 07 2017
%t A289440 a[n_]:=n*Max[Table[(Floor[(d - 1 - GCD[d, 3])/5] + 1)/d, {d, Divisors[n]}]]; Table[a[n], {n, 2, 100}] (* _Indranil Ghosh_, Jul 08 2017 *)
%o A289440 (PARI)
%o A289440 v(g,n,h)={my(t=0);fordiv(n,d,t=max(t,((d-1-gcd(d,g))\h + 1)*(n/d)));t}
%o A289440 a(n)=v(3,n,5); \\ _Andrew Howroyd_, Jul 07 2017
%o A289440 (Python)
%o A289440 from sympy import divisors, floor, gcd
%o A289440 def a(n): return n*max([(floor((d - 1 - gcd(d, 3))/5) + 1)/d for d in divisors(n)])
%o A289440 print([a(n) for n in range(2, 101)]) # _Indranil Ghosh_, Jul 08 2017
%Y A289440 Cf. A289439, A289441.
%K A289440 nonn
%O A289440 2,3
%A A289440 _N. J. A. Sloane_, Jul 07 2017
%E A289440 a(41)-a(70) from _Andrew Howroyd_, Jul 07 2017