A395746 Numbers m such that A265388(m) = A007947(m*(2*m-1)).

2, 3, 4, 5, 7, 9, 13, 15, 16, 19, 25, 27, 31, 37, 41, 49, 61, 64, 79, 97, 121, 139, 157, 169, 181, 199, 211, 229, 271, 289, 307, 313, 331, 337, 367, 379, 421, 439, 499, 547, 577, 601, 607, 619, 625, 661, 691, 727, 811, 829, 841, 877, 937, 967, 997, 1009, 1069

Offset

1,1

Comments

For m>1, A265388(m) <= A007947(m*(2*m-1)). This sequence lists the indices where this inequality is tight.

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000 (terms 1..226 from Vincenzo Librandi)

Mathematica

f[n_]:=Times@@(First/@FactorInteger[n]); g[n_]:=If[n==1, 0, GCD@@Table[Binomial[2 n, 2 k], {k, 1, n-1}]]; Select[Range[1100], g[#]==f[# (2 #-1)]&] (* Vincenzo Librandi, May 07 2026 *)

Prog

(Python)
from math import prod
from itertools import count, islice
from sympy.ntheory.factor_ import digits
from sympy import primefactors
def A395746_gen(startvalue=1): # generator of terms >= startvalue
    for n in count(max(startvalue, 1)):
        m = n*((k:=n<<1)-1)
        l = (~m & m-1).bit_length()
        ps = primefactors(m>>l)
        if (prod(ps)<<bool(l))==(prod((p if sum(digits(k, p)[1:])==2 else 1) for p in ps)<<(not(n&-n)^n) if n>1 else 0):
            yield n
A395746_list = list(islice(A395746_gen(), 50))
(Magma) rad := function(n) return &*PrimeDivisors(n); end function; h := function(n)
return n eq 1 select 0 else GCD([Binomial(2*n, 2*k) : k in [1..n-1]]); end function;
[m : m in [1..1100] | h(m) eq rad(m*(2*m-1))]; // Vincenzo Librandi, May 07 2026

Crossrefs

Cf. A007947, A265388.

Sequence in context: A117604 A117603 A250553 * A026450 A280451 A240178

Adjacent sequences: A395743 A395744 A395745 * A395747 A395748 A395749

Keyword

nonn

Author

Chai Wah Wu, May 05 2026

Status

approved