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

1,2

Comments

Conjecture: Complement of A072389.

Links

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

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[#]&]

Prog

(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

Crossrefs

Cf. A072389, A335572.

Sequence in context: A165332 A031179 A171521 * A092784 A047588 A213257

Adjacent sequences: A352793 A352794 A352795 * A352797 A352798 A352799

Keyword

nonn

Author

José María Grau Ribas, Jun 08 2022

Status

approved