A295661 Numbers with at least one odd exponent larger than one in their prime factorization.

8, 24, 27, 32, 40, 54, 56, 72, 88, 96, 104, 108, 120, 125, 128, 135, 136, 152, 160, 168, 184, 189, 200, 216, 224, 232, 243, 248, 250, 264, 270, 280, 288, 296, 297, 312, 328, 343, 344, 351, 352, 360, 375, 376, 378, 384, 392, 408, 416, 424, 432, 440, 456, 459, 472, 480, 486, 488, 500, 504, 512, 513, 520, 536, 540

Offset: 1

Author

Antti Karttunen, Nov 28 2017

Keywords

• nonn

Comments

The asymptotic density of this sequence is 1 - Product_{p prime} (1 - 1/(p^2*(p+1))) = 0.1184861602... (= 1 - A065465). - Amiram Eldar, May 18 2022

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Positions of nonzero terms in A295662 and A295663.

Subsequence of A046099 (64 = 2^6, although a cube, is not in this sequence).

Differs from A060476 (256 = 2^8 is not a member of this sequence).

Complement of A335275.

Cf. A065465.

Programs

Mathematica

Select[Range[540], Count[FactorInteger[#][[All, -1]], ?(And[OddQ@ #, # > 1] &)] > 0 &] (* _Michael De Vlieger, Nov 28 2017 *)

Python

from sympy import factorint
def ok(n):
    return max((e for e in factorint(n).values() if e%2), default=-1) > 1
print(list(filter(ok, range(541)))) # Michael S. Branicky, Aug 24 2021