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A273199 Integers which have a positive but not monotone difference table of their divisors.

%I A273199 #14 Feb 27 2020 11:50:06
%S A273199 51,55,57,69,87,93,111,119,123,129,141,159,177,183,201,207,213,219,
%T A273199 237,249,253,267,275,291,303,309,319,321,327,333,339,369,377,381,393,
%U A273199 403,411,417,447,453,471,489,501,519,537,543,573,579,591,597
%N A273199 Integers which have a positive but not monotone difference table of their divisors.
%C A273199 For an integer n>0 and not the unity we define DTD(n) to be the difference table of the divisors of n. We say that DTD(n) is positive if all entries in the table are positive and we call DTD(n) monotone if all rows and all columns of the table are nondecreasing (reading from left to right and from top to bottom).
%e A273199 159 is in this sequence because the DTD of 159 has only positive entries but not all columns are nondecreasing:
%e A273199 [  1   3   53 159]
%e A273199 [  2  50  106]
%e A273199 [ 48  56]
%e A273199 [  8]
%o A273199 (Sage)
%o A273199 def is_A273199(n):
%o A273199     D = divisors(n)
%o A273199     T = matrix(ZZ, len(D))
%o A273199     for (m, d) in enumerate(D):
%o A273199         T[0, m] = d
%o A273199         for k in range(m-1, -1, -1) :
%o A273199             T[m-k, k] = T[m-k-1, k+1] - T[m-k-1, k]
%o A273199             if T[m-k, k] <= 0: return False
%o A273199     non_decreasing = lambda L: all(x<=y for x, y in zip(L, L[1:]))
%o A273199     b = True
%o A273199     for k in range(0,len(D)-1):
%o A273199         b &= non_decreasing(T.row(k)[:len(D)-k])
%o A273199         b &= non_decreasing(T.column(k)[:len(D)-k])
%o A273199         if not b: return True
%o A273199     return False
%o A273199 print([n for n in range(1,600) if is_A273199(n)])
%Y A273199 Cf. A000040, A246655, A273102, A273130, A273200, A273201.
%K A273199 nonn
%O A273199 1,1
%A A273199 _Peter Luschny_, May 17 2016