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

1,1

Comments

Analog of the nontotients A005277.

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

Links

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

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A001615, A005277, A005382.

Sequence in context: A105041 A138632 A175957 * A060658 A239321 A054028

Adjacent sequences: A307052 A307053 A307054 * A307056 A307057 A307058

Keyword

nonn

Author

Torlach Rush, Mar 21 2019

Status

approved