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A352796 Numbers m such that {d + m/d : d | m } does not contain consecutive integers.

%I A352796 #37 Jul 11 2022 08:35:32
%S A352796 1,2,3,5,6,7,8,9,10,11,13,14,15,16,17,18,19,20,21,22,23,25,26,27,28,
%T A352796 29,30,31,32,33,34,35,37,38,39,41,42,43,44,45,46,47,48,49,50,51,52,53,
%U A352796 54,55,56,57,58,59,61,62,63,64,65,66,67,68,69,70,71,73,74
%N A352796 Numbers m such that {d + m/d : d | m } does not contain consecutive integers.
%C A352796 Conjecture: Complement of A072389.
%H A352796 Michel Marcus, <a href="/A352796/b352796.txt">Table of n, a(n) for n = 1..10000</a>
%t A352796 S[n_]:=Divisors[n]+n/Divisors[n]//Union; Test[n_]:= {aux=S[n];Union[ {False},Table[aux[[i+1]]-aux[[i]] ==1,{i,Length[aux]-1}]]}[[1]]   //Last; Select[Range[1000],Test[#]&]
%o A352796 (PARI) isok(m) = my(list=List()); fordiv(m, d, listput(list, d+m/d)); my(w = Set(vector(#list-1, k, list[k+1]-list[k]))); #select(x->(x==1), w) == 0; \\ _Michel Marcus_, Jun 09 2022
%o A352796 (Python)
%o A352796 from sympy import divisors
%o A352796 def ok(n):
%o A352796     s = sorted(set(d + n//d for d in divisors(n)))
%o A352796     return 1 not in set(s[i+1]-s[i] for i in range(len(s)-1))
%o A352796 print([k for k in range(1, 75) if ok(k)]) # _Michael S. Branicky_, Jul 10 2022
%Y A352796 Cf. A072389, A335572.
%K A352796 nonn
%O A352796 1,2
%A A352796 _José María Grau Ribas_, Jun 08 2022