A342478 Number k > 1 such that gpf(phi(k)/lambda(k)) = A006530(A000010(k)/A002322(k)) > log(log(k))^2.

2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 20, 21, 24, 28, 30, 32, 33, 35, 36, 39, 40, 42, 44, 45, 48, 51, 52, 55, 56, 57, 60, 63, 91, 117, 126, 133, 171, 182, 189, 217, 234, 247, 252, 259, 266, 273, 275, 279, 341, 451, 550, 671, 682, 775, 781, 825, 902

Offset

1,1

Comments

The asymptotic density of this sequence is 0 (Erdős et al., 1991).

Since log(log(k))^2 > 1 for k >= 16, the only terms of A033948 (numbers k such that phi(k) = lambda(k)) in this sequence are those below 16.

References

József Sándor and Borislav Crstici, Handbook of Number theory II, Kluwer Academic Publishers, 2004, Chapter 3, p. 194.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Paul Erdős, Carl Pomerance and Eric Schmutz, Carmichael's lambda function, Acta Arithmetica 58 (1991), pp. 363-385; alternative link.

Mathematica

p[n_] := FactorInteger[n][[-1, 1]]; q[n_] := p[EulerPhi[n]/CarmichaelLambda[n]] / Log[Log[n]]^2 > 1; Select[Range[1000], q]

Crossrefs

Cf. A000010, A002322, A006530, A033948, A034380.

Sequence in context: A124695 A005555 A128829 * A194967 A023770 A371864

Adjacent sequences: A342475 A342476 A342477 * A342479 A342480 A342481

Keyword

nonn

Author

Amiram Eldar, Mar 13 2021

Status

approved