A392165 Indices of record values in A392164.

1, 5, 19, 23, 37, 41, 59, 87, 101, 105, 113, 131, 151, 159, 167, 195, 203, 239, 259, 303, 307, 403, 451, 499, 517, 553, 573, 609, 645, 701, 719, 787, 807, 827, 889, 1003, 1055, 1067, 1103

Offset

1,2

Comments

Subsequence of A056911. - Chai Wah Wu, Jan 07 2026

Links

Table of n, a(n) for n=1..39.

Thomas Bloom, Problem #1109, Erdős Problems.

Thomas Bloom, Problem #1103, Erdős Problems.

Mathematica

f[n_]:=Length[FindClique[RelationGraph[SquareFreeQ[#1+#2]&&#1!=#2&, Select[Range[n], SquareFreeQ[2*#]&]]][[1]]];
Join[{1}, Select[Differences[Table[f[n], {n, 1, 400}]], #==1&->"Index"]+1]

Prog

(Python)
from itertools import count, islice
from networkx import empty_graph, find_cliques
from sympy import factorint
def A392165_gen(): # generator of terms
    def is_squarefree(n): return max(factorint(n).values(), default=1)<2
    c, G = 0, empty_graph([])
    for n in count(1, 2):
        if is_squarefree(n):
            G.add_node(n)
            G.add_edges_from((a, n) for a in G if a!=n and is_squarefree(a+n))
            if (m:=max(len(c) for c in find_cliques(G, nodes=[n])))>c:
                yield n
                c = m
A392165_list = list(islice(A392165_gen(), 20)) # Chai Wah Wu, Jan 07 2026

Crossrefs

Cf. A392164, A056911.

Sequence in context: A191609 A191084 A146509 * A062340 A167766 A106957

Adjacent sequences: A392162 A392163 A392164 * A392166 A392167 A392168

Keyword

nonn,more

Author

Elijah Beregovsky, Jan 02 2026

Extensions

a(22)-a(35) from Chai Wah Wu, Jan 07 2026

a(36)-a(39) from Chai Wah Wu, Jan 12 2026

Status

approved