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A321714 Numbers k such that lambda(k) = 12.

%I A321714 #25 Feb 28 2024 15:57:34
%S A321714 13,26,35,39,45,52,65,70,78,90,91,104,105,112,117,130,140,144,156,180,
%T A321714 182,195,208,210,234,260,273,280,312,315,336,360,364,390,420,455,468,
%U A321714 520,546,560,585,624,630,720,728,780,819,840,910,936,1008,1040,1092,1170,1260,1365,1456,1560,1638,1680,1820,1872,2184,2340,2520,2730,3120,3276,3640,4095,4368,4680,5040,5460,6552,7280,8190,9360,10920,13104,16380,21840,32760,65520
%N A321714 Numbers k such that lambda(k) = 12.
%C A321714 Here lambda is Carmichael's lambda function (see A002322).
%H A321714 R. D. Carmichael, <a href="https://doi.org/10.1090/S0002-9904-1910-01892-9">Note on a new number theory function</a>, Bull. Amer. Math. Soc. 16 (1910), 232-238.
%t A321714 Select[Range[65520], CarmichaelLambda[#] == 12 &] (* _Paolo Xausa_, Feb 28 2024 *)
%o A321714 (PARI)
%o A321714 lambda(n) = { \\ A002322
%o A321714   my(f=factor(n), fsz=matsize(f)[1]);
%o A321714   lcm(vector(fsz, k, my(p=f[k,1], e=f[k,2]);
%o A321714       if (p != 2, p^(e-1)*(p-1), e > 2, 2^(e-2), 2^(e-1))));
%o A321714 };
%o A321714 invlambda(n) = { \\ A270562
%o A321714   if (n <= 0, return(0), n==1, return(2), n%2, return(0));
%o A321714   my(f=factor(n), fsz=matsize(f)[1], g=1, h=1);
%o A321714   for (k=1, fsz, my(p=f[k,1], e=1);
%o A321714     while (n % lambda(p^e) == 0, e++); g *= p^(e-1));
%o A321714   fordiv(n, d, if (isprime(d+1) && g % (d+1) != 0, h *= (d+1)));
%o A321714   g *= h; if (lambda(g) != n, 0, g);
%o A321714 };
%o A321714 lambda_level(n) = {
%o A321714   my(N = invlambda(n)); if (!N, return([])); my(s=List());
%o A321714   fordiv(N, d, if (lambda(d) == n, listput(s, d)));
%o A321714   Set(s);
%o A321714 };
%o A321714 lambda_level(12)
%Y A321714 Cf. A002322, A270562, A321713.
%K A321714 nonn,fini,full
%O A321714 1,1
%A A321714 _Gheorghe Coserea_, Feb 21 2019