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A079065 In prime factorization of n replace odd primes with 3.

%I A079065 #19 Jul 13 2023 01:51:34
%S A079065 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,
%T A079065 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,
%U A079065 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
%N A079065 In prime factorization of n replace odd primes with 3.
%H A079065 Antti Karttunen, <a href="/A079065/b079065.txt">Table of n, a(n) for n = 1..65537</a>
%F A079065 Fully multiplicative with a(2) = 2, a(p) = 3 for odd primes p.
%F A079065 a(n) <= n; a(n)=n iff n is 3-smooth (A003586).
%F A079065 A065333(a(n)) = 1.
%F A079065 a(a(n)) = a(n).
%F A079065 A001221(a(n)) <= A001221(n).
%F A079065 A001222(a(n)) = A001222(n).
%F A079065 A006519(a(n)) = A006519(n).
%t A079065 a[n_] := 3^(PrimeOmega[n] - (e = IntegerExponent[n, 2])) * 2^e; Array[a, 100] (* _Amiram Eldar_, Jul 13 2023 *)
%o A079065 (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
%o A079065 (PARI) a(n) = my(e2 = valuation(n, 2)); 3^(bigomega(n) - e2)<<e2 \\ _David A. Corneth_, Sep 27 2018
%Y A079065 Cf. A001221, A001222, A003586, A006519, A065333.
%K A079065 nonn,mult
%O A079065 1,2
%A A079065 _Reinhard Zumkeller_, Feb 02 2003