A348431 a(n) = (n')^(n'), where ' is the arithmetic derivative of n.

1, 1, 1, 1, 256, 1, 3125, 1, 8916100448256, 46656, 823543, 1, 18446744073709551616, 1, 387420489, 16777216, 1461501637330902918203684832716283019655932542976, 1, 5842587018385982521381124421, 1, 1333735776850284124449081472843776, 10000000000, 302875106592253

Offset: 0

Author

Wesley Ivan Hurt, Oct 18 2021

Keywords

• nonn

Comments

a(p) = 1 for primes p since we have a(p) = (p')^(p') = 1^1 = 1.

Crossrefs

Cf. A000312, A003415, A068327.

Programs

Maple

a:= n-> (t-> t^t)(n*add(i[2]/i[1], i=ifactors(n)[2])):
seq(a(n), n=0..23);  # Alois P. Heinz, Oct 20 2021

Mathematica

Array[#^# &@ If[# < 2, 0, # Total[#2/#1 & @@@ FactorInteger[#]]] &, 19, 2] (* Michael De Vlieger, Oct 18 2021 *)

PARI

ad(n) = vecsum([n/f[1]*f[2]|f<-factor(n+!n)~]); \\ A003415
a(n) = my(d=ad(n)); d^d; \\ Michel Marcus, Oct 19 2021

Formula

a(n) = A000312(A003415(n)).