A323332 The Dedekind psi function values of the powerful numbers, A001615(A001694(n)).

1, 6, 12, 12, 24, 30, 36, 48, 72, 56, 96, 144, 108, 180, 216, 132, 150, 192, 288, 182, 336, 360, 432, 360, 324, 384, 576, 306, 648, 392, 380, 672, 720, 864, 672, 792, 900, 768, 552, 1152, 750, 1296, 1080, 1092, 972, 1344, 1440, 870, 1728, 2160, 992, 1584

Offset

1,2

Comments

The sum of the reciprocals of all the terms of this sequence is Pi^2/6 (A013661).

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

psi[1]=1; psi[n_] := n * Times@@(1+1/Transpose[FactorInteger[n]][[1]]); psi /@ Join[{1}, Select[Range@ 1200, Min@ FactorInteger[#][[All, 2]] > 1 &]] (* after T. D. Noe at A001615 and Harvey P. Dale at A001694 *)

Crossrefs

Cf. A001615, A001694, A013661, A082695, A112526.

Sequence in context: A315598 A224301 A181798 * A330922 A330921 A183688

Adjacent sequences: A323329 A323330 A323331 * A323333 A323334 A323335

Keyword

nonn

Author

Amiram Eldar, Jan 11 2019

Status

approved