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A273130 Numbers which have only positive entries in the difference table of their divisors.

%I A273130 #22 Feb 24 2020 15:40:37
%S A273130 1,2,3,4,5,7,8,9,11,13,16,17,19,21,23,25,27,29,31,32,33,37,39,41,43,
%T A273130 47,49,51,53,55,57,59,61,64,65,67,69,71,73,79,81,83,85,87,89,93,95,97,
%U A273130 101,103,107,109,111,113,115,119,121,123,125,127,128,129,131,133
%N A273130 Numbers which have only positive entries in the difference table of their divisors.
%C A273130 Primes and powers of primes are in the sequence.
%H A273130 Charles R Greathouse IV, <a href="/A273130/b273130.txt">Table of n, a(n) for n = 1..10000</a>
%e A273130 85 is in the sequence because the difference table of the divisors of 85 has only entries greater than 0:
%e A273130 [1, 5, 17, 85]
%e A273130 [4, 12, 68]
%e A273130 [8, 56]
%e A273130 [48]
%t A273130 Select[Range@ 1000, {} == NestWhile[ Differences, Divisors @ #, # != {} && Min[#] > 0 &] &] (* _Giovanni Resta_, May 16 2016 *)
%o A273130 (Sage)
%o A273130 def sf(z):
%o A273130     D = divisors(z)
%o A273130     T = matrix(ZZ, len(D))
%o A273130     for m, d in enumerate(D):
%o A273130         T[0, m] = d
%o A273130         for k in range(m-1, -1, -1) :
%o A273130             T[m-k, k] = T[m-k-1, k+1] - T[m-k-1, k]
%o A273130             if T[m-k, k] <= 0: return False
%o A273130     return True
%o A273130 print([z for z in range(1,100) if sf(z)])
%o A273130 (PARI) has(v)=if(#v<2, v[1]>0, if(vecmin(v)<1, 0, has(vector(#v-1,i,v[i+1]-v[i]))))
%o A273130 is(n)=has(divisors(n)) \\ _Charles R Greathouse IV_, May 16 2016
%Y A273130 Cf. A014567, A187202, A273102, A273103, A273109, A273157 (complement).
%K A273130 nonn
%O A273130 1,2
%A A273130 _Peter Luschny_, May 16 2016