cp's OEIS Frontend

A109290 Composite numbers which are not of the forms p*q -+ 1, where p and q are (not necessarily distinct) primes.

%I A109290 #12 Apr 21 2021 01:27:20
%S A109290 4,6,12,18,28,30,42,44,46,49,51,55,60,62,65,69,72,74,77,80,82,91,98,
%T A109290 99,100,102,104,106,108,111,115,125,126,129,136,138,148,150,152,153,
%U A109290 155,161,164,166,169,171,172,174,175,180,183,185,187,189,190,192,194,196
%N A109290 Composite numbers which are not of the forms p*q -+ 1, where p and q are (not necessarily distinct) primes.
%H A109290 Robert Israel, <a href="/A109290/b109290.txt">Table of n, a(n) for n = 1..10000</a>
%p A109290 filter:= proc(n)
%p A109290    if n::even then numtheory:-bigomega(n+1) <> 2 and numtheory:-bigomega(n-1) <> 2
%p A109290    elif n mod 4 = 1 then not isprime(n) and not isprime((n+1)/2)
%p A109290    else not isprime(n) and not isprime((n-1)/2)
%p A109290    fi
%p A109290 end proc:
%p A109290 select(filter, [$4..200]); # _Robert Israel_, Apr 20 2021
%t A109290 bo[n_] := Plus @@ Last /@ FactorInteger[n]; Select[Range[2, 200], ! (PrimeQ[ # ] || bo[ # - 1] == 2 || bo[ # + 1] == 2) &] (* _Ray Chandler_, Aug 27 2005 *)
%Y A109290 Cf. A109287, A109288, A109289.
%K A109290 nonn
%O A109290 1,1
%A A109290 _Giovanni Teofilatto_, Aug 20 2005
%E A109290 Corrected and extended by _Ray Chandler_, Aug 27 2005