A363123 Primitive terms of A363122: terms k of A363122 such that k/2 is not a term of A363122.

2, 12, 40, 56, 120, 144, 168, 176, 208, 280, 528, 544, 608, 624, 720, 736, 800, 840, 864, 880, 928, 992, 1008, 1040, 1232, 1456, 1584, 1632, 1824, 1872, 2208, 2288, 2368, 2400, 2624, 2640, 2720, 2752, 2784, 2976, 3008, 3040, 3120, 3136, 3392, 3680, 3696, 3776

Offset

1,1

Comments

If k is a term of this sequence then k*2^m is a term of A363122 for any m >= 0.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Maple

filter:= proc(n) local F2, Fp, v2, vp, t;
  F2, Fp:= selectremove(t -> t[1]=2, ifactors(n)[2]);
  if Fp = [] then return (n=2) fi;
  v2:= 2^F2[1, 2];
  vp:= max(map(t -> t[1]^t[2], Fp));
  v2 > vp and v2/2 <= vp;
end proc:
select(filter, [seq(i, i=2.10000, 2)]); # Robert Israel, May 18 2023

Mathematica

q[n_] := Module[{e = IntegerExponent[n, 2]}, 2^e > Max[Power @@@ FactorInteger[n/2^e]]]; Select[Range[2, 10000, 2], q[#] && ! q[#/2] &]

Prog

(PARI) is1(n) = {my(e = valuation(n, 2), m = n>>e); if(m == 1, n>1, f = factor(m); 2^e > vecmax(vector(#f~, i, f[i, 1]^f[i, 2]))); } \\ A363122
is(n) = !(n%2) && is1(n) && !is1(n/2)
(Python)
from itertools import count, islice
from sympy import factorint
def A363123_gen(startvalue=2): # generator of terms
    return filter(lambda n:(m:=n&-n)>max((p**e for p, e in factorint(n>>(~n&n-1).bit_length()).items()), default=1)>=m>>1, count(max(startvalue, 2)))
A363123_list = list(islice(A363123_gen(), 20)) # Chai Wah Wu, May 17 2023

Crossrefs

Cf. A363122.

Sequence in context: A190022 A086602 A019006 * A168057 A290131 A008911

Adjacent sequences: A363120 A363121 A363122 * A363124 A363125 A363126

Keyword

nonn,easy

Author

Amiram Eldar, May 16 2023

Status

approved