A292818 Numbers n such that psi(k) - phi(k) = 2*n has no solution.

6, 51, 57, 65, 77, 87, 93, 95, 117, 119, 123, 145, 147, 155, 161, 171, 177, 185, 187, 189, 203, 205, 207, 209, 215, 217, 219, 221, 237, 245, 247, 249, 255, 261, 267, 275, 287, 291, 297, 299, 301, 303, 305, 321, 325, 327, 329, 335, 341, 345, 357, 363, 365, 371, 377, 387

Offset

1,1

Comments

Inspired by a comment from Robert G. Wilson v.

All terms are composite.

Initial examples of forms of psi(k) - phi(k) where p, q, r, t are primes and a, b, c, d >= 1 as below:

If k = p^a, then psi(k) - phi(k) = 2*k/p.

If k = p^a*q^b, then psi(k) - phi(k) = 2*k*(p + q)/(p*q).

If k = p^a*q^b*r^c, then psi(k) - phi(k) = 2*k*(p*q + q*r + p*r + 1)/(p*q*r).

If k = p^a*q^b*r^c*t^d, then psi(k) - phi(k) = 2*k*(p*q*r + p*q*t + p*r*t + q*r*t + p + q + r + t)/(p*q*r*t).

Links

Table of n, a(n) for n=1..56.

Example

6 is a term because psi(k) - phi(k) = 12 has no solution for any possible form of k.

Mathematica

psi[n_] := If[n == 1, 1, n Times @@ (1 + 1/First /@ FactorInteger@ n)]; upto[n_] := Block[{d, T = 0 Range[n]}, Do[d = (psi[k] - EulerPhi[k])/2; If[d <= n, T[[d]] = 1], {k, 2, n^2}]; Flatten@ Position[T, 0]]; upto[387] (* Giovanni Resta, Sep 25 2017 *)

Crossrefs

Cf. A000010, A001615, A292786.

Sequence in context: A136383 A043084 A335704 * A173082 A113653 A133395

Adjacent sequences: A292815 A292816 A292817 * A292819 A292820 A292821

Keyword

nonn

Author

Altug Alkan, Sep 24 2017

Status

approved