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A115070
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a(n) = phi(n)/3^b(n), where b(n) is #{primes p=1 mod 3 dividing n}.
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1
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1, 1, 2, 2, 4, 2, 2, 4, 6, 4, 10, 4, 4, 2, 8, 8, 16, 6, 6, 8, 4, 10, 22, 8, 20, 4, 18, 4, 28, 8, 10, 16, 20, 16, 8, 12, 12, 6, 8, 16, 40, 4, 14, 20, 24, 22, 46, 16, 14, 20, 32, 8, 52, 18, 40, 8, 12, 28, 58, 16, 20, 10, 12, 32, 16, 20, 22, 32, 44, 8, 70, 24, 24, 12, 40, 12, 20, 8, 26, 32, 54
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OFFSET
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1,3
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COMMENTS
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Cubic analog of A070306. Always an integer.
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LINKS
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MAPLE
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with(numtheory):
a:= n-> phi(n)/3^add(`if`(irem(p, 3)=1, 1, 0), p=factorset(n)):
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MATHEMATICA
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b[n_] := Count[FactorInteger[n][[All, 1]], p_ /; Mod[p, 3] == 1];
a[n_] := EulerPhi[n]/3^b[n];
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PROG
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(PARI) {b(n)=my(f=factor(n)[, 1]); sum(i=1, #f, f[i]%3==1)};
{a(n)= eulerphi(n)/3^b(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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