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A327939
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Multiplicative with a(p^e) = p^(e-(e mod p)).
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12
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1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 16, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 27, 4, 1, 1, 1, 16, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 16, 1, 1, 1, 4, 1, 27, 1, 4, 1, 1, 1, 4, 1, 1, 1, 64, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 16, 27, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 16, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 108, 1, 1, 1, 16
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OFFSET
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1,4
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COMMENTS
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Fixed points of the map x -> gcd(x, A003415(x)), i.e., if we start iterating with A085731 from any x = n (>= 1), we will eventually reach a(n), after which the result does not change anymore. This was found by LODA miner (see C. Krause link), and is easily seen to be true by Eric M. Schmidt's multiplicative formula for A085731. Note also that this sequence is idempotent, meaning a(a(n)) = a(n) for all n. - Antti Karttunen, Apr 05 2021
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LINKS
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FORMULA
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Multiplicative with a(p^e) = p^(e-(e mod p)).
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MATHEMATICA
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f[p_, e_] := p^(e - Mod[e, p]); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Sep 14 2023 *)
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PROG
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(PARI) A327939(n) = { my(f = factor(n)); for(k=1, #f~, f[k, 2] = (f[k, 2]-(f[k, 2]%f[k, 1]))); factorback(f); };
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CROSSREFS
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Differs from A234957 for the first time at n=27.
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KEYWORD
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nonn,easy,mult
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AUTHOR
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STATUS
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approved
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