A289439 - OEIS

%I #26 Apr 24 2020 09:43:24

%S 1,1,2,1,3,2,4,3,5,2,6,3,7,5,8,4,9,4,10,7,11,5,12,5,13,9,14,6,15,6,16,

%T 11,17,10,18,8,19,13,20,8,21,9,22,15,23,10,24,14,25,17,26,11,27,11,28,

%U 19,29,12,30,12,31,21,32,15,33,14,34,23,35

%N The arithmetic function v_1(n,5).

%D J. Butterworth, Examining the arithmetic function v_g(n,h). Research Papers in Mathematics, B. Bajnok, ed., Gettysburg College, Vol. 8 (2008).

%H 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 a:= n-> n*max(seq((floor((d-2)/5)+1)/d, d=numtheory[divisors](n))):

%p seq(a(n), n=2..100);  # _Alois P. Heinz_, Jul 07 2017

%t a[n_]:=n*Max[Table[(Floor[(d - 2)/5] + 1)/d, {d, Divisors[n]}]]; Table[a[n], {n, 2, 100}] (* _Indranil Ghosh_, Jul 08 2017 *)

%o (PARI)

%o v(g,n,h)={my(t=0);fordiv(n,d,t=max(t,((d-1-gcd(d,g))\h + 1)*(n/d)));t}

%o a(n)=v(1,n,5); \\ _Andrew Howroyd_, Jul 07 2017

%o (Python)

%o from sympy import divisors, floor

%o def a(n): return int(n*max(int(floor((d - 2)/5) + 1)/d for d in divisors(n)))

%o print([a(n) for n in range(2, 101)]) # _Indranil Ghosh_, Jul 08 2017

%Y Cf. A289440, A289441.

%K nonn

%O 2,3

%A _N. J. A. Sloane_, Jul 07 2017

%E a(41)-a(70) from _Andrew Howroyd_, Jul 07 2017