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A255369
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a(n) = (sigma(n)-n-1)*(2-mu(n)), where sigma(n) is the sum of the divisors of n and mu(n) is the Möbius function.
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1
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-1, 0, 0, 4, 0, 5, 0, 12, 6, 7, 0, 30, 0, 9, 8, 28, 0, 40, 0, 42, 10, 13, 0, 70, 10, 15, 24, 54, 0, 123, 0, 60, 14, 19, 12, 108, 0, 21, 16, 98, 0, 159, 0, 78, 64, 25, 0, 150, 14, 84, 20, 90, 0, 130, 16, 126, 22, 31, 0, 214, 0, 33, 80, 124, 18, 231, 0, 114
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OFFSET
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1,4
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COMMENTS
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a(n) = 0 if and only if n is prime. If n is semiprime, then a(n) = sopfr(n).
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LINKS
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FORMULA
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MAPLE
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with(numtheory): a:=n->(sigma(n)-n-1)*(2-mobius(n)): seq(a(n), n=1..100);
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MATHEMATICA
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Table[(DivisorSigma[1, n] - n - 1) (2 - MoebiusMu[n]), {n, 100}]
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PROG
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(Magma) [(SumOfDivisors(n)-n-1)*(2-MoebiusMu(n)): n in [1..80]]; // Vincenzo Librandi, May 05 2015
(Perl) use ntheory ":all"; say +(divisor_sum($_)-$_-1)*(2-moebius($_)) for 1..80; # Dana Jacobsen, May 13 2015
(PARI) a(n)=(sigma(n)-n-1)*(2-moebius(n)) \\ Dana Jacobsen, May 13 2015
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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