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

1,3

Links

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

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.

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A191674 A238959 A238972 * A319579 A286631 A286243

Adjacent sequences: A207190 A207191 A207192 * A207194 A207195 A207196

Keyword

nonn

Author

Reinhard Zumkeller, Feb 16 2012

Status

approved