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

13, 26, 35, 39, 45, 52, 65, 70, 78, 90, 91, 104, 105, 112, 117, 130, 140, 144, 156, 180, 182, 195, 208, 210, 234, 260, 273, 280, 312, 315, 336, 360, 364, 390, 420, 455, 468, 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

Offset: 1

Author

Gheorghe Coserea, Feb 21 2019

Keywords

• nonn
• fini
• full

Comments

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

Links

• R. D. Carmichael, Note on a new number theory function, Bull. Amer. Math. Soc. 16 (1910), 232-238.

Crossrefs

Cf. A002322, A270562, A321713.

Programs

Mathematica

Select[Range[65520], CarmichaelLambda[#] == 12 &] (* Paolo Xausa, Feb 28 2024 *)

PARI

lambda(n) = { \\ A002322
  my(f=factor(n), fsz=matsize(f)[1]);
  lcm(vector(fsz, k, my(p=f[k,1], e=f[k,2]);
      if (p != 2, p^(e-1)*(p-1), e > 2, 2^(e-2), 2^(e-1))));
};
invlambda(n) = { \\ A270562
  if (n <= 0, return(0), n==1, return(2), n%2, return(0));
  my(f=factor(n), fsz=matsize(f)[1], g=1, h=1);
  for (k=1, fsz, my(p=f[k,1], e=1);
    while (n % lambda(p^e) == 0, e++); g *= p^(e-1));
  fordiv(n, d, if (isprime(d+1) && g % (d+1) != 0, h *= (d+1)));
  g *= h; if (lambda(g) != n, 0, g);
};
lambda_level(n) = {
  my(N = invlambda(n)); if (!N, return([])); my(s=List());
  fordiv(N, d, if (lambda(d) == n, listput(s, d)));
  Set(s);
};
lambda_level(12)