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A345266
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a(n) = Sum_{p|n, p prime} gcd(p,n/p).
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7
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0, 1, 1, 2, 1, 2, 1, 2, 3, 2, 1, 3, 1, 2, 2, 2, 1, 4, 1, 3, 2, 2, 1, 3, 5, 2, 3, 3, 1, 3, 1, 2, 2, 2, 2, 5, 1, 2, 2, 3, 1, 3, 1, 3, 4, 2, 1, 3, 7, 6, 2, 3, 1, 4, 2, 3, 2, 2, 1, 4, 1, 2, 4, 2, 2, 3, 1, 3, 2, 3, 1, 5, 1, 2, 6, 3, 2, 3, 1, 3, 3, 2, 1, 4, 2, 2, 2, 3, 1, 5, 2, 3, 2, 2, 2, 3, 1, 8, 4, 7, 1, 3, 1, 3, 3
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OFFSET
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1,4
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LINKS
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FORMULA
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a(p) = 1 for p prime.
If n is squarefree, then a(n) = omega(n).
a(p^k) = p for primes p and k >= 2. (End)
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EXAMPLE
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a(18) = Sum_{p|18} gcd(p,18/p) = gcd(2,9) + gcd(3,6) = 1 + 3 = 4.
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MATHEMATICA
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Table[Sum[GCD[k, n/k] (PrimePi[k] - PrimePi[k - 1]) (1 - Ceiling[n/k] + Floor[n/k]), {k, n}], {n, 100}]
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PROG
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(PARI) a(n) = my(f=factor(n), p); sum(k=1, #f~, p=f[k, 1]; gcd(p, n/p)); \\ Michel Marcus, Jun 16 2021
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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