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A351395
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Sum of the divisors of n that are either squarefree, prime powers, or both.
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1
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1, 3, 4, 7, 6, 12, 8, 15, 13, 18, 12, 16, 14, 24, 24, 31, 18, 21, 20, 22, 32, 36, 24, 24, 31, 42, 40, 28, 30, 72, 32, 63, 48, 54, 48, 25, 38, 60, 56, 30, 42, 96, 44, 40, 33, 72, 48, 40, 57, 43, 72, 46, 54, 48, 72, 36, 80, 90, 60, 76, 62, 96, 41, 127, 84, 144, 68, 58, 96, 144, 72
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = Sum_{d|n} d * sign(mu(d)^2 + [omega(d) = 1]).
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EXAMPLE
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a(36) = 25; 36 has 4 squarefree divisors 1,2,3,6 (where the primes 2 and 3 are both squarefree and 1st powers of primes) and 2 (additional) divisors that are powers of primes, 2^2 and 3^2. The sum of the divisors is then 1+2+3+4+6+9 = 25.
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MATHEMATICA
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Array[DivisorSum[#, #*Sign[MoebiusMu[#]^2 + Boole[PrimeNu[#] == 1]] &] &, 71] (* Michael De Vlieger, Feb 10 2022 *)
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PROG
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(PARI) a(n) = sumdiv(n, d, if (issquarefree(d) || isprimepower(d), d)); \\ Michel Marcus, Feb 10 2022
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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