A321714 - OEIS

%I #25 Feb 28 2024 15:57:34

%S 13,26,35,39,45,52,65,70,78,90,91,104,105,112,117,130,140,144,156,180,

%T 182,195,208,210,234,260,273,280,312,315,336,360,364,390,420,455,468,

%U 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 Numbers k such that lambda(k) = 12.

%C Here lambda is Carmichael's lambda function (see A002322).

%H 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 Select[Range[65520], CarmichaelLambda[#] == 12 &] (* _Paolo Xausa_, Feb 28 2024 *)

%o (PARI)

%o lambda(n) = { \\ A002322

%o   my(f=factor(n), fsz=matsize(f)[1]);

%o   lcm(vector(fsz, k, my(p=f[k,1], e=f[k,2]);

%o       if (p != 2, p^(e-1)*(p-1), e > 2, 2^(e-2), 2^(e-1))));

%o };

%o invlambda(n) = { \\ A270562

%o   if (n <= 0, return(0), n==1, return(2), n%2, return(0));

%o   my(f=factor(n), fsz=matsize(f)[1], g=1, h=1);

%o   for (k=1, fsz, my(p=f[k,1], e=1);

%o     while (n % lambda(p^e) == 0, e++); g *= p^(e-1));

%o   fordiv(n, d, if (isprime(d+1) && g % (d+1) != 0, h *= (d+1)));

%o   g *= h; if (lambda(g) != n, 0, g);

%o };

%o lambda_level(n) = {

%o   my(N = invlambda(n)); if (!N, return([])); my(s=List());

%o   fordiv(N, d, if (lambda(d) == n, listput(s, d)));

%o   Set(s);

%o };

%o lambda_level(12)

%Y Cf. A002322, A270562, A321713.

%K nonn,fini,full

%O 1,1

%A _Gheorghe Coserea_, Feb 21 2019