A289436 The arithmetic function v_1(n,4).

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

Offset: 2

Author

N. J. A. Sloane, Jul 07 2017

Keywords

• nonn

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.

Crossrefs

Cf. A289437, A289438.

Programs

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 *)

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 int(n*max(int(floor((d - 2)/4) + 1)/d for d in divisors(n)))
print([a(n) for n in range(2, 101)]) # Indranil Ghosh, Jul 08 2017

Extensions

a(41)-a(70) from Andrew Howroyd, Jul 07 2017