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A289435
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The arithmetic function v_3(n,3).
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113
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1, 0, 2, 2, 3, 2, 4, 2, 5, 4, 6, 4, 7, 6, 8, 6, 9, 6, 10, 6, 11, 8, 12, 10, 13, 8, 14, 10, 15, 10, 16, 12, 17, 14, 18, 12, 19, 12, 20, 14, 21, 14, 22, 18, 23, 16, 24, 16, 25, 18, 26, 18, 27, 22, 28, 18, 29, 20, 30, 20, 31, 20, 32, 26, 33, 22, 34, 24, 35
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OFFSET
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2,3
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REFERENCES
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J. Butterworth, Examining the arithmetic function v_g(n,h). Research Papers in Mathematics, B. Bajnok, ed., Gettysburg College, Vol. 8 (2008).
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LINKS
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MAPLE
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a:= n-> n*max(seq((floor((d-1-igcd(d, 3))/3)+1)
/d, d=numtheory[divisors](n))):
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MATHEMATICA
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a[n_]:=n*Max[Table[(Floor[(d - 1 - GCD[d, 3])/3] + 1)/d, {d, Divisors[n]}]]; Table[a[n], {n, 2, 100}] (* Indranil Ghosh, Jul 08 2017 *)
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PROG
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(PARI)
v(g, n, h)={my(t=0); fordiv(n, d, t=max(t, ((d-1-gcd(d, g))\h + 1)*(n/d))); t}
(Python)
from sympy import divisors, floor, gcd
def a(n): return n*max((floor((d - 1 - gcd(d, 3))/3) + 1)/d for d in divisors(n))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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