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