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A175496
Positive integers k where k is not squarefree but the number of divisors of k is a power of 2.
4
8, 24, 27, 40, 54, 56, 88, 104, 120, 125, 128, 135, 136, 152, 168, 184, 189, 216, 232, 248, 250, 264, 270, 280, 296, 297, 312, 328, 343, 344, 351, 375, 376, 378, 384, 408, 424, 440, 456, 459, 472, 488, 513, 520, 536, 552, 568, 584, 594, 616, 621, 632, 640
OFFSET
1,1
COMMENTS
This sequence is not the same as sequence A048109.
The asymptotic density of this sequence is A327839 - A059956 = 0.0799000375... - Amiram Eldar, Nov 01 2020
LINKS
MATHEMATICA
pow2Q[n_] := n == 2^IntegerExponent[n, 2]; aQ[n_] := ! SquareFreeQ[n] && pow2Q[DivisorSigma[0, n]]; Select[Range[640], aQ] (* Amiram Eldar, Sep 21 2019 *)
PROG
(PARI) isok(k) = my(d=numdiv(k)); !issquarefree(k) && (2^valuation(d, 2) == d); \\ Michel Marcus, Nov 20 2020
(Python)
from itertools import count, islice
from sympy import factorint
def A175496_gen(startvalue=2): # generator of terms >= startvalue
return filter(lambda n:max(f:=factorint(n).values())>1 and all(map(lambda m:not((k:=m+1)&-k)^k, f)), count(max(startvalue, 2)))
A175496_list = list(islice(A175496_gen(), 30)) # Chai Wah Wu, Jan 04 2023
CROSSREFS
Complement of A005117 within A036537.
Subsequence of A013929.
A048109, A062838\{1}, A113852 are subsequences.
Sequence in context: A336593 A176297 A375072 * A048109 A068781 A365864
KEYWORD
nonn
AUTHOR
Leroy Quet, May 30 2010
EXTENSIONS
Extended by D. S. McNeil, May 31 2010
STATUS
approved