cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A167192 Triangle read by rows: T(n,k) = (n-k)/gcd(n,k), 1 <= k <= n.

This page as a plain text file.
%I A167192 #25 Jan 13 2025 12:31:47
%S A167192 0,1,0,2,1,0,3,1,1,0,4,3,2,1,0,5,2,1,1,1,0,6,5,4,3,2,1,0,7,3,5,1,3,1,
%T A167192 1,0,8,7,2,5,4,1,2,1,0,9,4,7,3,1,2,3,1,1,0,10,9,8,7,6,5,4,3,2,1,0,11,
%U A167192 5,3,2,7,1,5,1,1,1,1,0,12,11,10,9,8,7,6,5,4,3,2,1,0,13,6,11,5,9,4,1,3,5,2,3
%N A167192 Triangle read by rows: T(n,k) = (n-k)/gcd(n,k), 1 <= k <= n.
%H A167192 Indranil Ghosh, <a href="/A167192/b167192.txt">Rows 1..120 of triangle, flattened</a>
%F A167192 T(n,k) = (n-k)/gcd(n,k), 1 <= k <= n.
%F A167192 T(n,k) = A025581(n,k)/A050873(n,k);
%F A167192 T(n,1) = A001477(n-1);
%F A167192 T(n,2) = A026741(n-2) for n > 1;
%F A167192 T(n,3) = A051176(n-3) for n > 2;
%F A167192 T(n,4) = A060819(n-4) for n > 4;
%F A167192 T(n,n-3) = A144437(n) for n > 3;
%F A167192 T(n,n-2) = A000034(n) for n > 2;
%F A167192 T(n,n-1) = A000012(n);
%F A167192 T(n,n) = A000004(n).
%e A167192 The triangle T(n,k) begins:
%e A167192 n\k   1   2   3   4  5  6  7  8  9 10 11 12 13  14  15 ...
%e A167192 1:    0
%e A167192 2:    1   0
%e A167192 3:    2   1   0
%e A167192 4:    3   1   1   0
%e A167192 5:    4   3   2   1  0
%e A167192 6:    5   2   1   1  1  0
%e A167192 7:    6   5   4   3  2  1  0
%e A167192 8:    7   3   5   1  3  1  1  0
%e A167192 9:    8   7   2   5  4  1  2  1  0
%e A167192 10:   9   4   7   3  1  2  3  1  1  0
%e A167192 11:  10   9   8   7  6  5  4  3  2  1  0
%e A167192 12:  11   5   3   2  7  1  5  1  1  1  1  0
%e A167192 13:  12  11  10   9  8  7  6  5  4  3  2  1  0
%e A167192 14:  13   6  11   5  9  4  1  3  5  2  3  1  1   0
%e A167192 15:  14  13   4  11  2  3  8  7  2  1  4  1  2   1   0
%e A167192 - _Wolfdieter Lang_, Feb 20 2013
%t A167192 Flatten[Table[(n-k)/GCD[n,k],{n,20},{k,n}]] (* _Harvey P. Dale_, Nov 27 2015 *)
%o A167192 (PARI) for(n=1,10, for(k=1,n, print1((n-k)/gcd(n,k), ", "))) \\ _G. C. Greubel_, Sep 13 2017
%Y A167192 Cf. A054531, A112543, A164306.
%K A167192 nonn,tabl
%O A167192 1,4
%A A167192 _Reinhard Zumkeller_, Oct 30 2009