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%I #40 Nov 12 2023 14:27:27
%S 8,12,18,20,27,28,44,45,50,52,63,68,75,76,92,98,99,116,117,124,125,
%T 147,148,153,164,171,172,175,188,207,212,236,242,244,245,261,268,275,
%U 279,284,292,316,325,332,333,338,343,356,363,369,387,388,404,412,423,425,428,436,452
%N Numbers with exactly three prime factors, not all distinct.
%C Cubes of primes together with products of a prime and the square of a different prime.
%C Numbers k for which A001222(k) = 3, but A001221(k) < 3. - _Antti Karttunen_, Apr 20 2017
%H Antti Karttunen, <a href="/A285508/b285508.txt">Table of n, a(n) for n = 1..10000</a>
%H Kalle Siukola, <a href="/A285508/a285508.txt">Python program</a>
%t Select[Range[452], PrimeOmega[#] == 3 && PrimeNu[#] < 3 &] (* _Giovanni Resta_, Apr 20 2017 *)
%o (PARI)
%o isA285508(n) = ((omega(n) < 3) && (bigomega(n) == 3));
%o n=0; k=1; while(k <= 10000, n=n+1; if(isA285508(n),write("b285508.txt", k, " ", n);k=k+1));
%o \\ _Antti Karttunen_, Apr 20 2017
%o (Scheme, with my IntSeq-library) (define A285508 (MATCHING-POS 1 1 (lambda (n) (and (= 3 (A001222 n)) (< (A001221 n) 3))))) ;; _Antti Karttunen_, Apr 20 2017
%o (Python)
%o from sympy import primefactors, primeomega
%o def omega(n): return len(primefactors(n))
%o def bigomega(n): return primeomega(n)
%o print([n for n in range(1, 501) if omega(n)<3 and bigomega(n) == 3]) # _Indranil Ghosh_, Apr 20 2017 and _Kalle Siukola_, Oct 25 2023
%Y Cf. A001221, A001222.
%Y Setwise difference of A014612 and A007304.
%Y Union of A030078 and A054753.
%K easy,nonn
%O 1,1
%A _Kalle Siukola_, Apr 20 2017
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