A123712 - OEIS

%I #22 Jul 15 2024 10:18:32

%S 60,84,90,120,126,132,140,150,156,168,180,198,204,220,228,234,240,252,

%T 260,264,270,276,280,294,300,306,308,312,315,336,340,342,348,350,360,

%U 364,372,378,380,396,408,414,440,444,450,456,460,468,476,480,490,492

%N Indices n such that 16 = A123709(n) = number of nonzero terms in row n of triangle A123706.

%C Triangle A123706 is the matrix inverse of triangle A010766, where A010766(n,k) = [n/k].

%C a(n) = A178212(n) for n <= 52, possibly more. [_Reinhard Zumkeller_, May 24 2010]

%C a(n) = A178212(n) for n <= 2000. - _Bill McEachen_, Jul 14 2024

%H G. C. Greubel, <a href="/A123712/b123712.txt">Table of n, a(n) for n = 1..1200</a>

%t Moebius[i_, j_] := If[Divisible[i, j], MoebiusMu[i/j], 0]; A123709[n_] := Length[Select[Table[Moebius[n, j] - Moebius[n, j + 1], {j, 1, n}], # != 0 &]]; Select[Range[6500], A123709[#] == 16 &] (* _G. C. Greubel_, Apr 22 2017 *)

%o (PARI)is(n)=my(M=matrix(n, n, r, c,r\c)^-1); sum(k=1, n, M[n, k]!=0)==16 \\ _Charles R Greathouse IV_, Feb 09 2012

%Y Cf. A123706, A123709, A123710, A123711, A010766.

%K nonn

%O 1,1

%A _Paul D. Hanna_, Oct 09 2006