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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 (list; graph; refs; listen; history; text; internal format)
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)>3||omega(n+1)>3), [1..1300])
CROSSREFS
Cf. A321494, A321495, A321496, A321497 (analog for 4, 5, 6, 7 factors).
Sequence in context: A251031 A256509 A259674 * A260282 A360358 A166841
KEYWORD
nonn
AUTHOR
M. F. Hasler, Nov 13 2018
STATUS
approved

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Last modified July 20 17:48 EDT 2024. Contains 374459 sequences. (Running on oeis4.)