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A289441 The arithmetic function v_5(n,5). 115
1, 1, 2, 0, 3, 2, 4, 3, 5, 2, 6, 3, 7, 5, 8, 4, 9, 4, 10, 7, 11, 5, 12, 4, 13, 9, 14, 6, 15, 6, 16, 11, 17, 10, 18, 8, 19, 13, 20, 8, 21, 9, 22, 15, 23, 10, 24, 14, 25, 17, 26, 11, 27, 10, 28, 19, 29, 12, 30, 12, 31, 21, 32, 15, 33, 14, 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-1-igcd(d, 5))/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, 5])/5] + 1)/d, {d, Divisors[n]}]]; Table[a[n], {n, 2, 100}] (* Indranil Ghosh, Jul 08 2017, after Maple code *)

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(5, 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, 5))/5) + 1)/d for d in divisors(n)])

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

CROSSREFS

Cf. A289439, A289440.

Sequence in context: A063749 A231333 A212175 * A291272 A291273 A008807

Adjacent sequences:  A289438 A289439 A289440 * A289442 A289443 A289444

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 14 22:45 EST 2019. Contains 329135 sequences. (Running on oeis4.)