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A289438 The arithmetic function v_4(n,4). 113
0, 1, 0, 1, 2, 2, 1, 3, 2, 3, 4, 3, 4, 5, 3, 4, 6, 5, 4, 7, 6, 6, 8, 6, 6, 9, 8, 7, 10, 8, 7, 11, 8, 10, 12, 9, 10, 13, 9, 10, 14, 11, 12, 15, 12, 12, 16, 14, 12, 17, 12, 13, 18, 15, 16, 19, 14, 15, 20, 15, 16, 21, 15, 16, 22, 17, 16, 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, 4))/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, 4])/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(4, 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, 4))/4) + 1)/d for d in divisors(n)])

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

CROSSREFS

Cf. A289436, A289437.

Sequence in context: A280716 A319444 A071285 * A008678 A159803 A058741

Adjacent sequences:  A289435 A289436 A289437 * A289439 A289440 A289441

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 16 03:44 EDT 2019. Contains 324145 sequences. (Running on oeis4.)