A289440 The arithmetic function v_3(n,5).

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, 6, 17, 10, 18, 8, 19, 9, 20, 8, 21, 9, 22, 10, 23, 10, 24, 14, 25, 12, 26, 11, 27, 11, 28, 12, 29, 12, 30, 12, 31, 18, 32, 15, 33, 14, 34, 15, 35

Offset

2,3

References

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

Links

Table of n, a(n) for n=2..70.

Bela Bajnok, Additive Combinatorics: A Menu of Research Problems, arXiv:1705.07444 [math.NT], May 2017. See Table in Section 1.6.1.

Maple

a:= n-> n*max(seq((floor((d-1-igcd(d, 3))/5)+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 - 1 - GCD[d, 3])/5] + 1)/d, {d, Divisors[n]}]]; Table[a[n], {n, 2, 100}] (* Indranil Ghosh, Jul 08 2017 *)

Prog

(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(3, n, 5); \\ Andrew Howroyd, Jul 07 2017
(Python)
from sympy import divisors, floor, gcd
def a(n): return n*max([(floor((d - 1 - gcd(d, 3))/5) + 1)/d for d in divisors(n)])
print([a(n) for n in range(2, 101)]) # Indranil Ghosh, Jul 08 2017

Crossrefs

Cf. A289439, A289441.

Sequence in context: A204539 A302604 A214270 * A290636 A106466 A130722

Adjacent sequences: A289437 A289438 A289439 * A289441 A289442 A289443

Keyword

nonn

Author

N. J. A. Sloane, Jul 07 2017

Extensions

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

Status

approved