

A321493


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.


7



714, 1364, 1595, 1770, 1785, 1869, 2001, 2090, 2145, 2184, 2210, 2261, 2345, 2379, 2414, 2639, 2805, 2820, 2849, 2870, 2925, 3002, 3009, 3059, 3080, 3219, 3255, 3289, 3354, 3366, 3444, 3450, 3485, 3534, 3654, 3689, 3705
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OFFSET

1,1


COMMENTS

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.
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!


LINKS



FORMULA



MATHEMATICA

aQ[n_]:=Module[{v={PrimeNu[n], PrimeNu[n+1]}}, Min[v]>2 && v!={3, 3}]; Select[Range[120000], aQ] (* Amiram Eldar, Nov 12 2018 *)


PROG

(PARI) select( is(n)=omega(n)>2&&omega(n+1)>2&&(omega(n)>3omega(n+1)>3), [1..1300])


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



