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A345344
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a(n) = Sum_{d^2|n} Omega(n/d^2).
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1
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0, 1, 1, 2, 1, 2, 1, 4, 2, 2, 1, 4, 1, 2, 2, 6, 1, 4, 1, 4, 2, 2, 1, 6, 2, 2, 4, 4, 1, 3, 1, 9, 2, 2, 2, 8, 1, 2, 2, 6, 1, 3, 1, 4, 4, 2, 1, 9, 2, 4, 2, 4, 1, 6, 2, 6, 2, 2, 1, 6, 1, 2, 4, 12, 2, 3, 1, 4, 2, 3, 1, 12, 1, 2, 4, 4, 2, 3, 1, 9, 6, 2, 1, 6, 2, 2, 2, 6, 1, 6, 2, 4, 2
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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) = Sum_{d^2|p} Omega(p/d^2) = Omega(p) = 1 for primes p.
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EXAMPLE
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a(24) = Sum_{d^2|24} Omega(24/d^2) = Omega(24) + Omega(6) = 4 + 2 = 6.
a(32) = Sum_{d^2|32} Omega(32/d^2) = Omega(32) + Omega(8) + Omega(2) = 5 + 3 + 1 = 9.
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MATHEMATICA
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Table[Sum[PrimeOmega[n/k^2] (1 - Ceiling[n/k^2] + Floor[n/k^2]), {k, n}], {n, 100}]
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PROG
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(PARI) a(n) = sumdiv(n, d, if (issquare(d), bigomega(n/d))); \\ Michel Marcus, Jun 14 2021
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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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