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A289437 The arithmetic function v_2(n,4). 113
0, 1, 1, 1, 2, 2, 2, 3, 2, 3, 4, 3, 4, 5, 4, 4, 6, 5, 5, 7, 6, 6, 8, 6, 6, 9, 8, 7, 10, 8, 8, 11, 8, 10, 12, 9, 10, 13, 10, 10, 14, 11, 12, 15, 12, 12, 16, 14, 12, 17, 13, 13, 18, 15, 16, 19, 14, 15, 20, 15, 16, 21, 16, 16, 22, 17, 17, 23, 20 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,5

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, 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 - 1 - GCD[d, 2])/4] + 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(2, n, 4); \\ Andrew Howroyd, Jul 07 2017

(Python)

from sympy import divisors, floor, gcd

def a(n): return n*max([(floor((d - 1 - gcd(d, 2))/4) + 1)/d for d in divisors(n)])

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

CROSSREFS

Cf. A289436, A289438.

Sequence in context: A219354 A026903 A253893 * A068324 A167505 A165015

Adjacent sequences:  A289434 A289435 A289436 * A289438 A289439 A289440

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 November 21 16:04 EST 2019. Contains 329371 sequences. (Running on oeis4.)