A069056 Numbers k such that Sum_{d|k} d^2*mu(d) divides k^2.

1, 12, 24, 36, 48, 72, 96, 108, 120, 144, 192, 216, 240, 288, 324, 336, 360, 384, 432, 480, 576, 600, 648, 672, 720, 768, 864, 960, 972, 1008, 1080, 1152, 1200, 1296, 1344, 1440, 1536, 1728, 1800, 1920, 1944, 2016, 2160, 2304, 2352, 2400, 2448, 2592, 2688

Offset

1,2

Comments

If n > 1, a(n+1) - a(n) == 0 (mod 12), so a(n+1) - a(n) = 12 for n=2,3,4,5,7,8,...; a(n+1) - a(n) = 24 for n=6,9,.... Conjecture: if c > 2 and n > 1, Sum_{d|n} d^c*mu(d) never divides n^c. Hence A063453(n) never divides n^3 for n > 1.

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Formula

Numbers k such that A046970(k) divides k.

Mathematica

f[d_] := d^2*MoebiusMu[d]; ok[n_] := Divisible[n^2, Total[f /@ Divisors[n]]]; Select[Range[3000], ok] (* Jean-François Alcover, Nov 15 2011 *)

Prog

(PARI) for(n=1, 1000, if(n^2%sumdiv(n, d, moebius(d)*d^2)==0, print1(n, ", ")))
(Haskell)
a069056 n = a069056_list !! (n-1)
a069056_list = filter (\x -> x ^ 2 `mod` a046970 x == 0) [1..]
-- Reinhard Zumkeller, Jan 19 2012

Crossrefs

Sequence in context: A141766 A364710 A367338 * A359434 A358693 A371413

Adjacent sequences: A069053 A069054 A069055 * A069057 A069058 A069059

Keyword

easy,nice,nonn

Author

Benoit Cloitre, Apr 07 2002

Status

approved