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

1,1

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A006519, A034699, A116882, A363123.

Subsequence of A174973.

Sequence in context: A326677 A330684 A070173 * A116882 A069519 A363948

Adjacent sequences: A363119 A363120 A363121 * A363123 A363124 A363125

Keyword

nonn,easy

Author

Amiram Eldar, May 16 2023

Status

approved