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A322361 a(n) = gcd(n, A003961(n)), where A003961 is completely multiplicative with a(prime(k)) = prime(k+1).

%I A322361 #18 Dec 24 2024 13:22:48
%S A322361 1,1,1,1,1,3,1,1,1,1,1,3,1,1,5,1,1,3,1,1,1,1,1,3,1,1,1,1,1,15,1,1,1,1,
%T A322361 7,9,1,1,1,1,1,3,1,1,5,1,1,3,1,1,1,1,1,3,1,1,1,1,1,15,1,1,1,1,1,3,1,1,
%U A322361 1,7,1,9,1,1,5,1,11,3,1,1,1,1,1,3,1,1,1,1,1,15,1,1,1,1,1,3,1,1,1,1,1,3,1,1,35
%N A322361 a(n) = gcd(n, A003961(n)), where A003961 is completely multiplicative with a(prime(k)) = prime(k+1).
%H A322361 Antti Karttunen, <a href="/A322361/b322361.txt">Table of n, a(n) for n = 1..20000</a>
%F A322361 a(n) = gcd(n, A003961(n)).
%F A322361 a(n) = A003961(gcd(n, A064989(n))).
%t A322361 a[n_] := If[n == 1, 1, GCD[n, Times@@(NextPrime[First[#]]^Last[#] &/@FactorInteger[n])]]; Array[a, 100] (* _Amiram Eldar_, Dec 05 2018 *)
%o A322361 (PARI)
%o A322361 A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From A003961
%o A322361 A322361(n) = gcd(n, A003961(n));
%o A322361 (Python)
%o A322361 from math import gcd, prod
%o A322361 from sympy import nextprime, factorint
%o A322361 def A322361(n): return gcd(n,prod(nextprime(p)**e for p, e in factorint(n).items())) # _Chai Wah Wu_, Dec 26 2022
%Y A322361 Cf. A003961, A064989, A318668, A322362.
%K A322361 nonn
%O A322361 1,6
%A A322361 _Antti Karttunen_, Dec 05 2018