A207193 Auxiliary function for computing the Carmichael lambda function (A002322).

1, 1, 2, 2, 4, 6, 2, 6, 10, 12, 4, 16, 18, 22, 20, 18, 28, 30, 8, 36, 40, 42, 46, 42, 52, 58, 60, 16, 66, 70, 72, 78, 54, 82, 88, 96, 100, 102, 106, 108, 112, 110, 100, 126, 32, 130, 136, 138, 148, 150, 156, 162, 166, 156, 172, 178, 180, 190, 192, 196, 198

Offset: 1

Author

Reinhard Zumkeller, Feb 16 2012

Keywords

• nonn

Links

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

Crossrefs

Cf. A000961, A002322, A025473, A025474, A085730.

Programs

Haskell

a207193 1 = 1
a207193 n | p == 2 && e > 2 = 2 ^ (e - 2)
          | otherwise       = (p - 1) * p ^ (e - 1)
          where p = a025473 n; e = a025474 n

Mathematica

f[p_, e_] := If[p == 2 && e > 2, 2^(e-2), (p-1)*p^(e-1)]; s[n_] := If[n == 1, 1, If[PrimePowerQ[n], f @@ (FactorInteger[n][[1]]), Nothing]]; Array[s, 200] (* Amiram Eldar, Apr 05 2025 *)

Formula

a(n) = f(A000961(n)), where f(1) = 1, and f(p^e) = 2^(e-2) if p = 2 and e > 2, and f(p^e) = (p-1)*p^(e-1) otherwise.