A294876 - OEIS

%I #12 Feb 22 2024 10:42:53

%S 1,2,2,6,2,8,2,18,10,8,2,72,2,8,8,126,2,200,2,72,8,8,2,648,22,8,50,72,

%T 2,128,2,882,8,8,8,23400,2,8,8,648,2,128,2,72,200,8,2,31752,34,968,8,

%U 72,2,5000,8,648,8,8,2,10368,2,8,200,16758,8,128,2,72,8,128,2,2737800,2,8,968,72,8,128,2,31752,1150,8,2,10368,8,8,8,648,2,80000,8,72

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

%H Antti Karttunen, <a href="/A294876/b294876.txt">Table of n, a(n) for n = 1..16384</a>

%F a(n) = Product_{d|n, d>1} A000040(gcd(d,n/d)).

%F Other identities. For all n >= 1:

%F 1+A007814(a(n)) = A034444(n).

%F 1+A056239(a(n)) = A055155(n).

%F For n > 1, A061395(a(n)) = A000188(n).

%t A294876[n_] := Product[Prime[GCD[d, n/d]], {d, Rest[Divisors[n]]}];

%t Array[A294876, 100] (* _Paolo Xausa_, Feb 22 2024 *)

%o (PARI) A294876(n) = { my(m=1); fordiv(n,d,if(d>1, m *= prime(gcd(d,n/d)))); m; };

%Y Cf. A294877 (rgs-version of this filter).

%Y Cf. A000040, A000188, A034444, A055155.

%Y Cf. also A293442, A293514, A293524.

%K nonn

%O 1,2

%A _Antti Karttunen_, Nov 11 2017