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

0,5

Comments

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

Links

Table of n, a(n) for n=0..22.

Formula

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

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 *)

Prog

(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

Crossrefs

Cf. A000312, A003415, A068327.

Sequence in context: A270876 A263166 A139305 * A351248 A160514 A203813

Adjacent sequences: A348428 A348429 A348430 * A348432 A348433 A348434

Keyword

nonn

Author

Wesley Ivan Hurt, Oct 18 2021

Status

approved