A307055 Even k such that psi(m) = k has no solution, where psi is the Dedekind psi function A001615.

2, 10, 16, 22, 26, 28, 34, 40, 46, 50, 52, 58, 64, 66, 70, 76, 78, 82, 86, 88, 92, 94, 100, 106, 116, 118, 122, 124, 130, 134, 136, 142, 146, 148, 154, 156, 166, 170, 172, 178, 184, 188, 190, 196, 202, 206, 208, 210, 214, 218, 220, 226, 232, 236, 238, 244, 246, 250

Offset: 1

Author

Torlach Rush, Mar 21 2019

Keywords

• nonn

Comments

Analog of the nontotients A005277.

Contains 2*p if p is in A307390. - Robert Israel, Apr 17 2019

Examples

			2 is a term because there exists no m such that psi(m) = 2.
4 is not a term because 4 = 3*(3+1)/3.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001615, A005277, A005382.

Programs

Maple

N:= 1000: # to get all terms <= N
psi:= proc(n) local p; n*mul(1+1/p, p=numtheory:-factorset(n)) end proc:
sort(convert({seq(i,i=2..N,2)} minus map(psi, {$1..N}), list)); # Robert Israel, Apr 17 2019

Mathematica

M = 1000; (* to get all terms <= M *)
psi[n_] := n Sum[MoebiusMu[d]^2/d, {d, Divisors[n]}];
Range[2, M, 2] ~Complement~ (psi /@ Range[M]) (* Jean-François Alcover, Aug 01 2020, after Maple *)

PARI

dpsi(n) = = n * sumdivmult(n, d, issquarefree(d)/d); \\ A001615
isok(n) = {if (!(n%2), for (k=1, n-1,  if (dpsi(k) == n, return(0));); return (1););} \\ Michel Marcus, Mar 22 2019