A175496 Positive integers k where k is not squarefree but the number of divisors of k is a power of 2.

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

Author

Leroy Quet, May 30 2010

Keywords

• nonn

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

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

Crossrefs

Cf. A059956, A327839.

Complement of A005117 within A036537.

Subsequence of A013929.

A048109, A062838\{1}, A113852 are subsequences.

Programs

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 *)

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

Extensions

Extended by D. S. McNeil, May 31 2010