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A323332 The Dedekind psi function values of the powerful numbers, A001615(A001694(n)). 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 9 18:43 EDT 2021. Contains 343744 sequences. (Running on oeis4.)