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A292818 Numbers n such that psi(k) - phi(k) = 2*n has no solution. 0
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 (list; graph; refs; listen; history; text; internal format)
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 A113653 * A173082 A133395 A050916

Adjacent sequences:  A292815 A292816 A292817 * A292819 A292820 A292821

KEYWORD

nonn

AUTHOR

Altug Alkan, Sep 24 2017

STATUS

approved

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Last modified February 16 21:59 EST 2019. Contains 320200 sequences. (Running on oeis4.)