A294876 a(n) = Product_{d|n, d>1} prime(gcd(d,n/d)).

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

Offset: 1

Author

Antti Karttunen, Nov 11 2017

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384

Crossrefs

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

Cf. A000040, A000188, A034444, A055155.

Cf. also A293442, A293514, A293524.

Programs

Mathematica

A294876[n_] := Product[Prime[GCD[d, n/d]], {d, Rest[Divisors[n]]}];
Array[A294876, 100] (* Paolo Xausa, Feb 22 2024 *)

PARI

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

Formula

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

Other identities. For all n >= 1:

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

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

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