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A295661
Numbers with at least one odd exponent larger than one in their prime factorization.
5
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
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 A240111 A301517
KEYWORD
nonn
AUTHOR
Antti Karttunen, Nov 28 2017
STATUS
approved