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A289438
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The arithmetic function v_4(n,4).
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113
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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)
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OFFSET
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2,5
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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, 4))/4)+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, 4])/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, gcd
def a(n): return n*max([(floor((d - 1 - gcd(d, 4))/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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