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

1,2

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.

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A355557 A329738 A133296 * A076402 A053198 A249278

Adjacent sequences: A323330 A323331 A323332 * A323334 A323335 A323336

Keyword

nonn

Author

Amiram Eldar, Jan 11 2019

Status

approved