A325449 Psi-untouchable numbers: impossible values for A306927(n) = A001615(n) - n.

30, 38, 58, 60, 66, 94, 98, 102, 118, 120, 132, 138, 146, 158, 174, 178, 188, 190, 204, 206, 222, 238, 240, 246, 262, 264, 276, 278, 282, 290, 292, 298, 306, 318, 322, 326, 338, 348, 354, 374, 380, 390, 398, 402, 406, 408, 426, 430, 444, 458, 462, 474, 476, 478

Offset: 1

Author

Amiram Eldar, Sep 06 2019

Keywords

• nonn

Comments

Analogous to untouchable numbers (A005114) with Dedekind psi function (A001615) instead of the sum of divisors function, sigma (A000203).

te Riele named these numbers psi_1-untouchable. He calculated the first 2896 terms (terms below 20000). He proved that this sequence is infinite by showing that all the numbers of the form 2^k*3*5 (k >= 1, A110286(k) except for k = 0) are psi-untouchables.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• H. J. J. te Riele, A theoretical and computational study of generalized aliquot sequences (Doctoral thesis), MCT-74, Mathematisch Centrum, Amsterdam, 1976, Chapter 9.

Crossrefs

Cf. A001615, A005114, A110286, A306927.

Programs

Mathematica

f[1] = 0; f[n_] := n*(Times @@ (1 + 1/FactorInteger[n][[;; , 1]]) - 1); m = 300; v = Table[0, {m}]; Do[j = f[k]; If[2 <= j <= m, v[[j]]++], {k, 1, m^2}]; Rest[Position[v, _?(# == 0 &)] // Flatten]