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A348994 a(n) = A003961(n) / gcd(n, A003961(n)), where A003961(n) is fully multiplicative with a(prime(k)) = prime(k+1).

%I A348994 #16 Nov 28 2021 12:53:30
%S A348994 1,3,5,9,7,5,11,27,25,21,13,15,17,33,7,81,19,25,23,63,55,39,29,45,49,
%T A348994 51,125,99,31,7,37,243,65,57,11,25,41,69,85,189,43,55,47,117,35,87,53,
%U A348994 135,121,147,95,153,59,125,91,297,115,93,61,21,67,111,275,729,119,65,71,171,145,33,73,75,79,123,49,207
%N A348994 a(n) = A003961(n) / gcd(n, A003961(n)), where A003961(n) is fully multiplicative with a(prime(k)) = prime(k+1).
%C A348994 Numerator of ratio A003961(n) / n. This ratio is fully multiplicative, and a(n) / A348990(n) = A319626(A003961(n)) / A319627(A003961(n)) gives it in its lowest terms.
%H A348994 Antti Karttunen, <a href="/A348994/b348994.txt">Table of n, a(n) for n = 1..20000</a>
%H A348994 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A348994 a(n) = A003961(n) / gcd(n, A003961(n)).
%F A348994 a(n) = A319626(A003961(n)).
%t A348994 Array[#2/GCD[##] & @@ {#, If[# == 1, 1, Times @@ Map[NextPrime[#1]^#2 & @@ # &, FactorInteger[#]]]} &, 76] (* _Michael De Vlieger_, Nov 11 2021 *)
%o A348994 (PARI)
%o A348994 A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
%o A348994 A348994(n) = (A003961(n) / gcd(n, A003961(n)));
%Y A348994 Cf. A003961, A319626, A319627, A348990 (denominators).
%K A348994 nonn,frac
%O A348994 1,2
%A A348994 _Antti Karttunen_, Nov 10 2021