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

%I A207193 #16 Apr 05 2025 09:11:06
%S A207193 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,
%T A207193 60,16,66,70,72,78,54,82,88,96,100,102,106,108,112,110,100,126,32,130,
%U A207193 136,138,148,150,156,162,166,156,172,178,180,190,192,196,198
%N A207193 Auxiliary function for computing the Carmichael lambda function (A002322).
%H A207193 Reinhard Zumkeller, <a href="/A207193/b207193.txt">Table of n, a(n) for n = 1..10000</a>
%F A207193 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.
%t A207193 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 *)
%o A207193 (Haskell)
%o A207193 a207193 1 = 1
%o A207193 a207193 n | p == 2 && e > 2 = 2 ^ (e - 2)
%o A207193           | otherwise       = (p - 1) * p ^ (e - 1)
%o A207193           where p = a025473 n; e = a025474 n
%Y A207193 Cf. A000961, A002322, A025473, A025474, A085730.
%K A207193 nonn
%O A207193 1,3
%A A207193 _Reinhard Zumkeller_, Feb 16 2012