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A279457 Numbers n such that number of distinct primes dividing n is odd and number of prime divisors (counted with multiplicity) of n is odd. 4
2, 3, 5, 7, 8, 11, 13, 17, 19, 23, 27, 29, 30, 31, 32, 37, 41, 42, 43, 47, 53, 59, 61, 66, 67, 70, 71, 73, 78, 79, 83, 89, 97, 101, 102, 103, 105, 107, 109, 110, 113, 114, 120, 125, 127, 128, 130, 131, 137, 138, 139, 149, 151, 154, 157, 163, 165, 167, 168, 170, 173, 174, 179, 180, 181, 182, 186, 190, 191, 193, 195, 197, 199, 211 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Intersection of A026424 and A030230.
Numbers n such that A000035(A001221(n)) = 1 and A000035(A001222(n)) = 1.
Numbers n such that A076479(n) = -1 and A008836(n) = -1.
All primes (A000040) are included in the sequence.
LINKS
Eric Weisstein's World of Mathematics, Prime Factor
Eric Weisstein's World of Mathematics, Distinct Prime Factors
EXAMPLE
27 is in the sequence because 27 = 3^3 therefore omega(27) = 1 {3} is odd and bigomega(27) = 3 {3,3,3} is odd.
MATHEMATICA
Select[Range[220], Mod[PrimeNu[#1], 2] == Mod[PrimeOmega[#1], 2] == 1 & ]
Select[Range[300], AllTrue[{PrimeNu[#], PrimeOmega[#]}, OddQ]&] (* Harvey P. Dale, Jul 10 2023 *)
CROSSREFS
Sequence in context: A066720 A079851 A060634 * A359891 A171561 A246551
KEYWORD
nonn,easy
AUTHOR
Ilya Gutkovskiy, Dec 12 2016
STATUS
approved

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)