cp's OEIS Frontend

A273195 The determinant of the difference table of the divisors vanishes for these numbers.

%I A273195 #18 Feb 27 2020 11:51:28
%S A273195 10,28,50,99,110,130,170,171,190,196,222,230,250,290,310,370,410,430,
%T A273195 470,476,530,532,550,590,610,644,650,670,710,730,790,812,830,850,868,
%U A273195 890,950,970
%N A273195 The determinant of the difference table of the divisors vanishes for these numbers.
%C A273195 Prime power-like numbers (A273200) have nonvanishing determinants.
%e A273195 50 is in this sequence because the determinant of DTD(50) = 0.
%e A273195 [  1  2  5 10 25 50]
%e A273195 [  1  3  5 15 25  0]
%e A273195 [  2  2 10 10  0  0]
%e A273195 [  0  8  0  0  0  0]
%e A273195 [  8 -8  0  0  0  0]
%e A273195 [-16  0  0  0  0  0]
%t A273195 selQ[n_] := Module[{d = Divisors[n], ld}, ld = Length[d]; Det @ Table[ PadRight[ Differences[d, k], ld], {k, 0, ld-1}] == 0];
%t A273195 Select[Range[1000], selQ] (* _Jean-François Alcover_, Jul 15 2019 *)
%o A273195 (Sage)
%o A273195 def is_A273195(n):
%o A273195     D = divisors(n)
%o A273195     T = matrix(ZZ, len(D))
%o A273195     for (m, d) in enumerate(D):
%o A273195         T[0, m] = d
%o A273195         for k in range(m-1, -1, -1) :
%o A273195             T[m-k, k] = T[m-k-1, k+1] - T[m-k-1, k]
%o A273195     return T.det() == 0
%o A273195 print([n for n in range(1, 1000) if is_A273195(n)])
%Y A273195 Cf. A273200.
%K A273195 nonn
%O A273195 1,1
%A A273195 _Peter Luschny_, May 18 2016