A323333 The Euler phi function values of the powerful numbers, A000010(A001694(n)).

1, 2, 4, 6, 8, 20, 18, 16, 12, 42, 32, 24, 54, 40, 36, 110, 100, 64, 48, 156, 84, 80, 72, 120, 162, 128, 96, 272, 108, 294, 342, 168, 160, 144, 252, 220, 200, 256, 506, 192, 500, 216, 360, 312, 486, 336, 320, 812, 288, 240, 930, 440, 324, 400, 512, 660, 600

Offset: 1

Author

Amiram Eldar, Jan 11 2019

Keywords

• nonn

Comments

The sum of the reciprocals of all the terms of this sequence is Murata's constant Product_{p prime}(1 + 1/(p-1)^2) (A065485).

Sequence is injective: no value occurs more than once. - Amiram Eldar and Antti Karttunen, Sep 30 2019

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Eckford Cohen, A property of Dedekind's psi-function, Proceedings of the American Mathematical Society, Vol. 12, No. 6 (1961), p. 996.

Crossrefs

Cf. A000010, A001694, A002618 (a subsequence), A065485, A082695, A112526, A323332.

Programs

Mathematica

EulerPhi /@ Join[{1}, Select[Range@ 1200, Min@ FactorInteger[#][[All, 2]] > 1 &]] (* after Harvey P. Dale at A001694 *)

PARI

lista(nn) = apply(x->eulerphi(x), select(x->ispowerful(x), vector(nn, k, k))); \\ Michel Marcus, Jan 11 2019