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A348360
a(n) = Product_{d|n} d^(d'), where ' is the arithmetic derivative.
0
1, 2, 3, 512, 5, 46656, 7, 35184372088832, 1594323, 100000000, 11, 2208245755649745670373376, 13, 289254654976, 38443359375, 11972621413014756705924586149611790497021399392059392, 17, 5689644950987917544474214347285987328, 19
OFFSET
1,2
FORMULA
a(p) = p for primes p since we have a(p) = 1^1' * p^p' = 1^0 * p^1 = p.
EXAMPLE
a(4) = 512; a(4) = Product_{d|4} d^d' = 1^1' * 2^2' * 4^4' = 1^0 * 2^1 * 4^4 = 1 * 2 * 256 = 512.
MATHEMATICA
Array[Times @@ Map[#^If[# < 2, 0, # Total[#2/#1 & @@@ FactorInteger[#]]] &, Divisors[#]] &, 19] (* Michael De Vlieger, Oct 14 2021 *)
CROSSREFS
Cf. A003415.
Sequence in context: A196070 A173342 A090510 * A004887 A240709 A264577
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Oct 14 2021
STATUS
approved