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A289441
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The arithmetic function v_5(n,5).
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115
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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)
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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, 5))/5)+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, 5])/5] + 1)/d, {d, Divisors[n]}]]; Table[a[n], {n, 2, 100}] (* Indranil Ghosh, Jul 08 2017, after Maple code *)
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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, 5))/5) + 1)/d for d in divisors(n)])
print([a(n) for n in range(2, 101)]) # Indranil Ghosh, Jul 08 2017, after Maple code
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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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