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A079065
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In prime factorization of n replace odd primes with 3.
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2
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1, 2, 3, 4, 3, 6, 3, 8, 9, 6, 3, 12, 3, 6, 9, 16, 3, 18, 3, 12, 9, 6, 3, 24, 9, 6, 27, 12, 3, 18, 3, 32, 9, 6, 9, 36, 3, 6, 9, 24, 3, 18, 3, 12, 27, 6, 3, 48, 9, 18, 9, 12, 3, 54, 9, 24, 9, 6, 3, 36, 3, 6, 27, 64, 9, 18, 3, 12, 9, 18, 3, 72, 3, 6, 27, 12, 9, 18, 3, 48, 81, 6, 3, 36, 9, 6, 9, 24, 3
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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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Fully multiplicative with a(2) = 2, a(p) = 3 for odd primes p.
a(n) <= n; a(n)=n iff n is 3-smooth (A003586).
a(a(n)) = a(n).
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MATHEMATICA
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a[n_] := 3^(PrimeOmega[n] - (e = IntegerExponent[n, 2])) * 2^e; Array[a, 100] (* Amiram Eldar, Jul 13 2023 *)
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PROG
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(PARI) A079065(n) = { my(f=factor(n)); for(i=1, #f~, if(f[i, 1]%2, f[i, 1] = 3)); factorback(f); }; \\ Antti Karttunen, Sep 27 2018
(PARI) a(n) = my(e2 = valuation(n, 2)); 3^(bigomega(n) - e2)<<e2 \\ David A. Corneth, Sep 27 2018
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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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