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A348990 a(n) = n / gcd(n, A003961(n)), where A003961(n) is fully multiplicative function with a(prime(k)) = prime(k+1).

%I A348990 #22 Nov 28 2021 12:53:07
%S A348990 1,2,3,4,5,2,7,8,9,10,11,4,13,14,3,16,17,6,19,20,21,22,23,8,25,26,27,
%T A348990 28,29,2,31,32,33,34,5,4,37,38,39,40,41,14,43,44,9,46,47,16,49,50,51,
%U A348990 52,53,18,55,56,57,58,59,4,61,62,63,64,65,22,67,68,69,10,71,8,73,74,15,76,7,26,79,80,81,82,83,28
%N A348990 a(n) = n / gcd(n, A003961(n)), where A003961(n) is fully multiplicative function with a(prime(k)) = prime(k+1).
%C A348990 Denominator of ratio A003961(n) / n. This ratio is fully multiplicative, and A348994(n) / a(n) = A319626(A003961(n)) / A319627(A003961(n)) gives it in its lowest terms.
%H A348990 Antti Karttunen, <a href="/A348990/b348990.txt">Table of n, a(n) for n = 1..20000</a>
%H A348990 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A348990 a(n) = n / A322361(n) = n / gcd(n, A003961(n)).
%F A348990 a(n) = A319627(A003961(n)).
%F A348990 For all odd numbers n, a(n) = A003961(A319627(n)).
%F A348990 For all n >= 1, A000035(A348990(n)) = A000035(n). [Preserves the parity]
%t A348990 Array[#1/GCD[##] & @@ {#, Times @@ Map[NextPrime[#1]^#2 & @@ # &, FactorInteger[#]]} &, 84] (* _Michael De Vlieger_, Nov 11 2021 *)
%o A348990 (PARI)
%o A348990 A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
%o A348990 A348990(n) = (n/gcd(n, A003961(n)));
%Y A348990 Cf. A000035, A000961, A002110, A003961, A319626, A319627, A319630 (fixed points), A322361, A349169 (where equal to A348992).
%Y A348990 Cf. A348994 (numerators).
%K A348990 nonn,frac
%O A348990 1,2
%A A348990 _Antti Karttunen_, Nov 10 2021