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A289436 The arithmetic function v_1(n,4). 113
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 (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-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 *)

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(1, n, 4); \\ Andrew Howroyd, Jul 07 2017

(Python)

from sympy import divisors, floor

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

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

CROSSREFS

Cf. A289437, A289438.

Sequence in context: A257909 A289439 A213633 * A282745 A097140 A028242

Adjacent sequences:  A289433 A289434 A289435 * A289437 A289438 A289439

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 June 25 10:10 EDT 2019. Contains 324351 sequences. (Running on oeis4.)