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A319522
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Completely multiplicative with a(prime(2*k)) = prime(k) and a(prime(2*k-1)) = 1 for any k > 0 (where prime(k) denotes the k-th prime number).
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3
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1, 1, 2, 1, 1, 2, 3, 1, 4, 1, 1, 2, 5, 3, 2, 1, 1, 4, 7, 1, 6, 1, 1, 2, 1, 5, 8, 3, 11, 2, 1, 1, 2, 1, 3, 4, 13, 7, 10, 1, 1, 6, 17, 1, 4, 1, 1, 2, 9, 1, 2, 5, 19, 8, 1, 3, 14, 11, 1, 2, 23, 1, 12, 1, 5, 2, 1, 1, 2, 3, 29, 4, 1, 13, 2, 7, 3, 10, 31, 1, 16, 1
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OFFSET
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1,3
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COMMENTS
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See A319521 for a similar sequence and additional comments.
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LINKS
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FORMULA
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a(n) <= n with equality iff n = 1.
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EXAMPLE
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a(42) = a(prime(1)) * a(prime(2)) * a(prime(4)) = 1 * prime(1) * prime(2) = 6.
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PROG
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(PARI) a(n) = my (f=factor(n)); prod(i=1, #f~, my (pi=primepi(f[i, 1])); if (pi%2==0, prime(pi/2)^f[i, 2], 1))
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CROSSREFS
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KEYWORD
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nonn,mult
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AUTHOR
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STATUS
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approved
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