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A279457
Numbers k such that number of distinct primes dividing k is odd and number of prime divisors (counted with multiplicity) of k 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
OFFSET
1,1
COMMENTS
Intersection of A026424 and A030230.
Numbers k such that A000035(A001221(k)) = 1 and A000035(A001222(k)) = 1.
Numbers k such that A076479(k) = -1 and A008836(k) = -1.
All primes (A000040) are included in the sequence.
LINKS
Eric Weisstein's World of Mathematics, Distinct Prime Factors.
Eric Weisstein's World of Mathematics, Prime Factor.
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 *)
PROG
(PARI) is(k) = {my(f = factor(k)); omega(f) % 2 && bigomega(f) % 2; } \\ Amiram Eldar, Sep 17 2024
KEYWORD
nonn,easy
AUTHOR
Ilya Gutkovskiy, Dec 12 2016
STATUS
approved