

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

M. F. Hasler, Table of n, a(n) for n = 1..5000


FORMULA

A321503 \ A140077.


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

Cf. A140077, A321503.
Cf. A321494, A321495, A321496, A321497 (analog for 4, 5, 6, 7 factors).
Sequence in context: A251031 A256509 A259674 * A260282 A166841 A166829
Adjacent sequences: A321490 A321491 A321492 * A321494 A321495 A321496


KEYWORD

nonn


AUTHOR

M. F. Hasler, Nov 13 2018


STATUS

approved



