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A294895 a(n) = Product_{d|n, gcd(d,n/d)>1} prime(gcd(d,n/d)-1).

%I A294895 #16 Feb 22 2024 10:41:41
%S A294895 1,1,1,2,1,1,1,4,3,1,1,4,1,1,1,20,1,9,1,4,1,1,1,16,7,1,9,4,1,1,1,100,
%T A294895 1,1,1,396,1,1,1,16,1,1,1,4,9,1,1,400,13,49,1,4,1,81,1,16,1,1,1,16,1,
%U A294895 1,9,1700,1,1,1,4,1,1,1,17424,1,1,49,4,1,1,1,400,171,1,1,16,1,1,1,16,1,81,1,4,1,1,1,10000,1,169,9,4508,1,1,1,16,1
%N A294895 a(n) = Product_{d|n, gcd(d,n/d)>1} prime(gcd(d,n/d)-1).
%C A294895 For all i, j: a(i) = a(j) => A294897(i) = A294897(j).
%H A294895 Antti Karttunen, <a href="/A294895/b294895.txt">Table of n, a(n) for n = 1..16384</a>
%F A294895 a(n) = Product_{d|n} A008578(gcd(d,n/d)).
%F A294895 a(n) = A064989(A294876(n)).
%F A294895 For n >= 1, A001222(a(n)) = A048105(n).
%F A294895 For n > 1, 1+A061395(a(n)) = A000188(n).
%t A294895 A294895[n_] := Times @@ Prime[Select[Map[GCD[#, n/#] &, Divisors[n]], #>1 &] - 1];
%t A294895 Array[A294895, 100] (* _Paolo Xausa_, Feb 22 2024 *)
%o A294895 (PARI) A294895(n) = { my(m=1); fordiv(n,d,if(gcd(d,n/d)>1, m *= prime(gcd(d,n/d)-1))); m; };
%Y A294895 Cf. A005117 (the positions of ones).
%Y A294895 Cf. A294876, A294897.
%K A294895 nonn
%O A294895 1,4
%A A294895 _Antti Karttunen_, Nov 21 2017