A192083 Arithmetic derivative of squares of prime powers: a(n) = A003415(A056798(n)).

0, 4, 6, 32, 10, 14, 192, 108, 22, 26, 1024, 34, 38, 46, 500, 1458, 58, 62, 5120, 74, 82, 86, 94, 1372, 106, 118, 122, 24576, 134, 142, 146, 158, 17496, 166, 178, 194, 202, 206, 214, 218, 226, 5324, 18750, 254, 114688, 262, 274, 278, 298, 302, 314, 326, 334

Offset: 1

Author

Reinhard Zumkeller, Jun 26 2011

Keywords

• nonn

Comments

A001787 and A024622 give record values and where they occur.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A003415, A024622, A025473, A025474, A056798, A192084.

Subsequences: A001787, A027471, A051674, A079705, A100484.

Programs

Mathematica

s[n_] := If[PrimePowerQ[n], f = FactorInteger[n][[1]]; 2*f[[2]]*n^(2 - 1/f[[2]]), Nothing]; s[1] = 0; Array[s, 200] (* Amiram Eldar, Apr 06 2025 *)

Formula

a(n) = 2 * A025474(n) * A025473(n)^(2*A025474(n) - 1).

A192084(n) = A003415(a(n)).