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A279458
Numbers k such that number of distinct primes dividing k is even and number of prime divisors (counted with multiplicity) of k is even.
4
1, 6, 10, 14, 15, 21, 22, 24, 26, 33, 34, 35, 36, 38, 39, 40, 46, 51, 54, 55, 56, 57, 58, 62, 65, 69, 74, 77, 82, 85, 86, 87, 88, 91, 93, 94, 95, 96, 100, 104, 106, 111, 115, 118, 119, 122, 123, 129, 133, 134, 135, 136, 141, 142, 143, 144, 145, 146, 152, 155, 158, 159, 160, 161, 166, 177, 178, 183, 184, 185, 187, 189
OFFSET
1,2
COMMENTS
Intersection of A028260 and A030231.
Numbers k such that A000035(A001221(k)) = 0 and A000035(A001222(k)) = 0.
Numbers k such that A076479(k) = 1 and A008836(k) = 1.
LINKS
Eric Weisstein's World of Mathematics, Distinct Prime Factors.
Eric Weisstein's World of Mathematics, Prime Factor.
EXAMPLE
24 is in the sequence because 24 = 2^3*3 therefore omega(24) = 2 {2,3} is even and bigomega(24) = 4 {2,2,2,3} is even.
MATHEMATICA
Select[Range[220], Mod[PrimeNu[#1], 2] == Mod[PrimeOmega[#1], 2] == 0 & ]
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