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A294876
a(n) = Product_{d|n, d>1} prime(gcd(d,n/d)).
7
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
1,2
LINKS
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).
MATHEMATICA
A294876[n_] := Product[Prime[GCD[d, n/d]], {d, Rest[Divisors[n]]}];
Array[A294876, 100] (* Paolo Xausa, Feb 22 2024 *)
PROG
(PARI) A294876(n) = { my(m=1); fordiv(n, d, if(d>1, m *= prime(gcd(d, n/d)))); m; };
CROSSREFS
Cf. A294877 (rgs-version of this filter).
Cf. also A293442, A293514, A293524.
Sequence in context: A193322 A165460 A242649 * A293514 A028330 A293524
KEYWORD
nonn
AUTHOR
Antti Karttunen, Nov 11 2017
STATUS
approved