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

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, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 73, 74

Offset: 1

Author

José María Grau Ribas, Jun 08 2022

Keywords

• nonn

Comments

Conjecture: Complement of A072389.

Links

• Michel Marcus, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A072389, A335572.

Programs

Mathematica

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[#]&]

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

Python

from sympy import divisors
def ok(n):
    s = sorted(set(d + n//d for d in divisors(n)))
    return 1 not in set(s[i+1]-s[i] for i in range(len(s)-1))
print([k for k in range(1, 75) if ok(k)]) # Michael S. Branicky, Jul 10 2022