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A289435 The arithmetic function v_3(n,3). 113
1, 0, 2, 2, 3, 2, 4, 2, 5, 4, 6, 4, 7, 6, 8, 6, 9, 6, 10, 6, 11, 8, 12, 10, 13, 8, 14, 10, 15, 10, 16, 12, 17, 14, 18, 12, 19, 12, 20, 14, 21, 14, 22, 18, 23, 16, 24, 16, 25, 18, 26, 18, 27, 22, 28, 18, 29, 20, 30, 20, 31, 20, 32, 26, 33, 22, 34, 24, 35 (list; graph; refs; listen; history; text; internal format)
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))/3)+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])/3] + 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, 3); \\ Andrew Howroyd, Jul 07 2017

(Python)

from sympy import divisors, floor, gcd

def a(n): return n*max([(floor((d - 1 - gcd(d, 3))/3) + 1)/d for d in divisors(n)])

print map(a, xrange(2, 101)) # Indranil Ghosh, Jul 08 2017

CROSSREFS

Cf. A211316 (equals v_1(n,3)).

Sequence in context: A117658 A325564 A323888 * A067540 A218701 A305790

Adjacent sequences:  A289432 A289433 A289434 * A289436 A289437 A289438

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jul 06 2017

EXTENSIONS

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

STATUS

approved

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Last modified June 16 10:03 EDT 2019. Contains 324152 sequences. (Running on oeis4.)