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

1,1

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

Mathematica

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

Prog

(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

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.

Sequence in context: A374590 A325990 A060476 * A376142 A377844 A240111

Adjacent sequences: A295658 A295659 A295660 * A295662 A295663 A295664

Keyword

nonn

Author

Antti Karttunen, Nov 28 2017

Status

approved