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%I #14 Nov 22 2018 14:31:21
%S 714,1364,1595,1770,1785,1869,2001,2090,2145,2184,2210,2261,2345,2379,
%T 2414,2639,2805,2820,2849,2870,2925,3002,3009,3059,3080,3219,3255,
%U 3289,3354,3366,3444,3450,3485,3534,3654,3689,3705
%N Numbers m such that m and m+1 both have at least 3, but m or m+1 has at least 4 distinct prime factors.
%C A321503 lists numbers m such that m and m+1 both have at least 3 distinct prime factors, while A140077 lists numbers such that m and m+1 have exactly 3 distinct prime factors. This sequence is the complement of the latter in the former, it consists of terms with indices (15, 60, 82, 98, 99, 104, ...) of the former.
%C Since m and m+1 can't share a prime factor, we have a(n)*(a(n)+1) >= p(3+4)# = A002110(7). Remarkably enough, a(1) = A000196(A002110(3+4)) exactly!
%H M. F. Hasler, <a href="/A321493/b321493.txt">Table of n, a(n) for n = 1..5000</a>
%F A321503 \ A140077.
%t aQ[n_]:=Module[{v={PrimeNu[n],PrimeNu[n+1]}},Min[v]>2 && v!={3,3}]; Select[Range[120000], aQ] (* _Amiram Eldar_, Nov 12 2018 *)
%o (PARI) select( is(n)=omega(n)>2&&omega(n+1)>2&&(omega(n)>3||omega(n+1)>3), [1..1300])
%Y Cf. A140077, A321503.
%Y Cf. A321494, A321495, A321496, A321497 (analog for 4, 5, 6, 7 factors).
%K nonn
%O 1,1
%A _M. F. Hasler_, Nov 13 2018
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