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Triangle read by rows: T(n,k) = (n mod d(k)), where d(i) is the number of divisors of i.
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%I #18 Sep 07 2016 00:17:29

%S 0,0,0,0,1,1,0,0,0,1,0,1,1,2,1,0,0,0,0,0,2,0,1,1,1,1,3,1,0,0,0,2,0,0,

%T 0,0,0,1,1,0,1,1,1,1,0,0,0,0,1,0,2,0,2,1,2,0,1,1,2,1,3,1,3,2,3,1,0,0,

%U 0,0,0,0,0,0,0,0,0,0,0,1,1

%N Triangle read by rows: T(n,k) = (n mod d(k)), where d(i) is the number of divisors of i.

%H G. C. Greubel, <a href="/A154234/b154234.txt">Table of n, a(n) for the first 50 rows</a>

%e The first few rows are given by:

%e 0.

%e 0 0.

%e 0 1 1.

%e 0 0 0 1.

%e 0 1 1 2 1.

%e 0 0 0 0 0 2.

%e 0 1 1 1 1 3 1.

%e 0 0 0 2 0 0 0 0.

%e 0 1 1 0 1 1 1 1 0.

%e 0 0 0 1 0 2 0 2 1 2.- _G. C. Greubel_, Sep 06 2016

%t Table[Mod[n,DivisorSigma[0,k]],{n,20},{k,n}]//Flatten (* _Harvey P. Dale_, Jul 21 2016 *)

%o (PARI) T(n,k)=n%numdiv(k) \\ _Charles R Greathouse IV_, Sep 07 2016

%Y Cf. A000005.

%K nonn,tabl,easy

%O 1,14

%A _Juri-Stepan Gerasimov_, Nov 26 2010