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A289436
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The arithmetic function v_1(n,4).
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113
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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
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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-2)/4)+1)/d, d=numtheory[divisors](n))):
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MATHEMATICA
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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 *)
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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
def a(n): return int(n*max(int(floor((d - 2)/4) + 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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