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A289440 The arithmetic function v_3(n,5). 113
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 (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))/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

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Last modified August 4 01:48 EDT 2020. Contains 336201 sequences. (Running on oeis4.)