A291931 Primitive elements of A290002.

1, 10, 18, 54, 70, 78, 110, 162, 174, 198, 222, 230, 234, 246, 294, 414, 426, 438, 450, 470, 486, 534, 594, 666, 702, 770, 846, 858, 882, 910, 1070, 1158, 1218, 1242, 1314, 1350, 1458, 1610, 1722, 1782, 1794, 1866, 1914, 1926, 1938, 1950, 1998, 2058, 2106, 2250, 2442, 2530, 2538, 2574, 2590, 2646, 2886

Offset

1,2

Comments

Members k of A290002 such that k/2 is not in A290002.

Includes all members of A025192 except 2 and 6.

Links

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

Example

a(3) = 18 is in the sequence because psi(phi(18)) = phi(psi(18)) = 12 but psi(phi(9)) = 12 <> 4 = phi(psi(9)).

Maple

psi:= proc(n)  n*mul((1+1/i[1]), i=ifactors(n)[2]) end:
A290002:= select(psi @ numtheory:-phi = numtheory:-phi @ psi, {$1..3000}):
sort(convert(A290002 minus map(`*`, A290002, 2), list));

Mathematica

f[n_] := n Sum[MoebiusMu[d]^2/d, {d, Divisors@ n}]; With[{s = Select[Range[3000], f[EulerPhi@ #] == EulerPhi[f@ #] &]}, Select[s, FreeQ[s, #/2] &]] (* Michael De Vlieger, Sep 06 2017 *)

Crossrefs

Cf. A025192, A290002.

Sequence in context: A301326 A350317 A255603 * A050576 A144376 A266708

Adjacent sequences: A291928 A291929 A291930 * A291932 A291933 A291934

Keyword

nonn

Author

Robert Israel, Sep 06 2017

Status

approved