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A384372 Numbers m such that both m-1 and m+1 are the product of at least 4 not necessarily distinct primes.

%I A384372 #32 Jun 14 2025 21:45:03
%S A384372 55,89,127,151,161,197,199,209,233,249,251,271,295,305,307,329,341,
%T A384372 343,349,351,377,379,391,415,449,461,463,485,487,489,491,511,521,545,
%U A384372 551,559,569,571,593,631,649,665,685,687,689,701,703,713,727,737,739,749,751
%N A384372 Numbers m such that both m-1 and m+1 are the product of at least 4 not necessarily distinct primes.
%C A384372 Numbers m such that bigomega(m-1) >= 4 and bigomega(m+1) >= 4.
%e A384372 55 is in the sequence because 55-1 = 2*3^3 and 55+1 = 2^3*7 are both products of at least 4 primes.
%e A384372 71 is not in the sequence because 71-1 = 2*5*7.
%p A384372 q:= n-> andmap(x-> numtheory[bigomega](x)>3, [n-1, n+1]):
%p A384372 select(q, [$1..991])[];  # _Alois P. Heinz_, Jun 12 2025
%o A384372 (Python)
%o A384372 from sympy import primeomega
%o A384372 def ok(n): return n>1 and primeomega(n-1)>3 and primeomega(n+1)>3
%o A384372 print(list(filter(ok, range(520))))
%o A384372 (PARI) isok(m) = (m>1) && (bigomega(m-1)>3) && (bigomega(m+1)>3); \\ _Michel Marcus_, Jun 12 2025
%Y A384372 Cf. A001222, A176462.
%K A384372 nonn
%O A384372 1,1
%A A384372 _Sinuhe Perea_, May 27 2025