A360325 - OEIS

%I #11 Feb 04 2023 14:14:53

%S 1,1,3,1,5,3,1,1,9,5,11,3,1,1,15,1,17,9,1,5,3,11,1,3,25,1,27,1,1,15,

%T 31,1,33,17,5,9,1,1,3,5,41,3,1,11,45,1,1,3,1,25,51,1,1,27,55,1,3,1,59,

%U 15,1,31,9,1,5,33,67,17,3,5,1,9,1,1,75,1,11,3,1

%N a(n) is the largest divisor of n that has only prime-indexed prime factors.

%H Amiram Eldar, <a href="/A360325/b360325.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = 1 if and only if n is in A320628.

%F a(n) = n if and only if n is in A076610.

%F a(n) = n/A360329(n).

%F Multiplicative with a(p^e) = p^e if p is a prime-indexed prime (A006450), and 1 otherwise.

%t f[p_, e_] := If[PrimeQ[PrimePi[p]], p^e, 1]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]

%o (PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, if(isprime(primepi(f[i, 1])), f[i, 1]^f[i, 2], 1)); }

%Y Cf. A006450, A076610, A320628, A360326, A360327, A360329.

%K nonn,mult

%O 1,3

%A _Amiram Eldar_, Feb 03 2023