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