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A307055
Even k such that psi(m) = k has no solution, where psi is the Dedekind psi function A001615.
2
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
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
KEYWORD
nonn
AUTHOR
Torlach Rush, Mar 21 2019
STATUS
approved