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A289441 The arithmetic function v_5(n,5).

%I A289441 #19 Apr 23 2020 11:19:36
%S A289441 1,1,2,0,3,2,4,3,5,2,6,3,7,5,8,4,9,4,10,7,11,5,12,4,13,9,14,6,15,6,16,
%T A289441 11,17,10,18,8,19,13,20,8,21,9,22,15,23,10,24,14,25,17,26,11,27,10,28,
%U A289441 19,29,12,30,12,31,21,32,15,33,14,34,23,35
%N A289441 The arithmetic function v_5(n,5).
%D A289441 J. Butterworth, Examining the arithmetic function v_g(n,h). Research Papers in Mathematics, B. Bajnok, ed., Gettysburg College, Vol. 8 (2008).
%H A289441 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 A289441 a:= n-> n*max(seq((floor((d-1-igcd(d, 5))/5)+1)
%p A289441         /d, d=numtheory[divisors](n))):
%p A289441 seq(a(n), n=2..100);  # _Alois P. Heinz_, Jul 07 2017
%t A289441 a[n_]:=n*Max[Table[(Floor[(d - 1 - GCD[d, 5])/5] + 1)/d, {d, Divisors[n]}]]; Table[a[n], {n, 2, 100}] (* _Indranil Ghosh_, Jul 08 2017, after Maple code *)
%o A289441 (PARI)
%o A289441 v(g,n,h)={my(t=0);fordiv(n,d,t=max(t,((d-1-gcd(d,g))\h + 1)*(n/d)));t}
%o A289441 a(n)=v(5,n,5); \\ _Andrew Howroyd_, Jul 07 2017
%o A289441 (Python)
%o A289441 from sympy import divisors, floor, gcd
%o A289441 def a(n): return n*max([(floor((d - 1 - gcd(d, 5))/5) + 1)/d for d in divisors(n)])
%o A289441 print([a(n) for n in range(2, 101)]) # _Indranil Ghosh_, Jul 08 2017, after Maple code
%Y A289441 Cf. A289439, A289440.
%K A289441 nonn
%O A289441 2,3
%A A289441 _N. J. A. Sloane_, Jul 07 2017
%E A289441 a(41)-a(70) from _Andrew Howroyd_, Jul 07 2017