A363122 Numbers k such that the highest power of 2 dividing k is larger than the highest power of p dividing k for any odd prime p.

2, 4, 8, 12, 16, 24, 32, 40, 48, 56, 64, 80, 96, 112, 120, 128, 144, 160, 168, 176, 192, 208, 224, 240, 256, 280, 288, 320, 336, 352, 384, 416, 448, 480, 512, 528, 544, 560, 576, 608, 624, 640, 672, 704, 720, 736, 768, 800, 832, 840, 864, 880, 896, 928, 960, 992

Offset: 1

Author

Amiram Eldar, May 16 2023

Keywords

• nonn
• easy

Comments

Numbers k such that A006519(k) = A034699(k).

If k is a term of this sequence then k*2^m is a term for any m >= 0. The primitive terms are in A363123.

Links

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

Crossrefs

Cf. A006519, A034699, A116882, A363123.

Subsequence of A174973.

Programs

Mathematica

q[n_] := Module[{e = IntegerExponent[n, 2]}, 2^e > Max[Power @@@ FactorInteger[n/2^e]]]; Select[Range[1000], q]

PARI

is(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]))); }

Python

from itertools import count, islice
from sympy import factorint
def A363122_gen(startvalue=2): # generator of terms >= startvalue
    return filter(lambda n:n&-n>max((p**e for p, e in factorint(n>>(~n&n-1).bit_length()).items()),default=0),count(max(startvalue,2)))
A363122_list = list(islice(A363122_gen(),20)) # Chai Wah Wu, May 17 2023