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A164306 Triangle read by rows: T(n, k) = k / gcd(k, n), 1 <= k <= n.

%I A164306 #17 Sep 20 2022 14:23:36
%S A164306 1,1,1,1,2,1,1,1,3,1,1,2,3,4,1,1,1,1,2,5,1,1,2,3,4,5,6,1,1,1,3,1,5,3,
%T A164306 7,1,1,2,1,4,5,2,7,8,1,1,1,3,2,1,3,7,4,9,1,1,2,3,4,5,6,7,8,9,10,1,1,1,
%U A164306 1,1,5,1,7,2,3,5,11,1,1,2,3,4,5,6,7,8,9,10,11,12,1
%N A164306 Triangle read by rows: T(n, k) = k / gcd(k, n), 1 <= k <= n.
%C A164306 Also the gcd of the coefficients of the partition polynomials (called 'De Moivre polynomials' by O'Sullivan, see link, Theorem 4.1). - _Peter Luschny_, Sep 20 2022
%H A164306 Indranil Ghosh, <a href="/A164306/b164306.txt">Rows 1..120 of triangle, flattened</a>.
%H A164306 Cormac O'Sullivan, <a href="https://arxiv.org/abs/2203.02868">De Moivre and Bell polynomials</a>, arXiv:2203.02868 [math.CO], 2022.
%F A164306 Sum of n-th row = A057661(n).
%F A164306 T(n, k) = A051537(n, k)/A054531(n, k). - _Reinhard Zumkeller_, Oct 30 2009
%e A164306 From _Indranil Ghosh_, Feb 14 2017: (Start)
%e A164306 Triangle begins:
%e A164306 1,
%e A164306 1, 1,
%e A164306 1, 2, 1,
%e A164306 1, 1, 3, 1,
%e A164306 1, 2, 3, 4, 1,
%e A164306 1, 1, 1, 2, 5, 1,
%e A164306 1, 2, 3, 4, 5, 6, 1,
%e A164306 . . .
%e A164306 T(4,3) = 3 / gcd(3,4) = 3 / 1 = 3. (End)
%p A164306 seq(seq(k / igcd(n, k), k = 1..n), n = 1..13); # _Peter Luschny_, Sep 20 2022
%t A164306 Flatten[Table[k/GCD[k,n],{n,20},{k,n}]] (* _Harvey P. Dale_, Jul 21 2013 *)
%o A164306 (PARI) for(n=0,10, for(k=1,n, print1(k/gcd(k,n), ", "))) \\ _G. C. Greubel_, Sep 13 2017
%Y A164306 Cf. A051537, A054531, A057661, A167192.
%K A164306 nonn,tabl
%O A164306 1,5
%A A164306 _Reinhard Zumkeller_, Aug 12 2009