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A321503 Numbers m such that m and m+1 both have at least 3 distinct prime factors. 6

%I

%S 230,285,429,434,455,494,560,594,609,615,644,645,650,665,714,740,741,

%T 759,804,805,819,825,854,860,884,902,935,945,969,986,987,1001,1014,

%U 1022,1034,1035,1044,1064,1065,1070,1085,1104,1105,1130,1196,1209,1220,1221,1235,1239,1245,1265

%N Numbers m such that m and m+1 both have at least 3 distinct prime factors.

%C Disjoint union of A140077 (omega({m, m+1}} = {3}) and A321493 (not both have exactly 3 prime divisors). The latter contains terms with indices {15, 60, 82, 98, 99, 104, ...} of this sequence.

%C Numbers m and m+1 can never have a common prime factor (consider them mod p), therefore the terms are > sqrt(A002110(3+3)), A002110 = primorial.

%H M. F. Hasler, <a href="/A321503/b321503.txt">Table of n, a(n) for n = 1..10000</a>

%t aQ[n_]:=Module[{v={PrimeNu[n], PrimeNu[n+1]}}, Min[v]>2]; Select[Range[1300], aQ] (* Amiram Eldar, Nov 12 2018 *)

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

%Y Cf. A255346, A321504 .. A321506, A321489 (analog for k = 2, ..., 7 prime divisors).

%Y Cf. A321493, A321494 .. A321497 (subsequences of the above: m or m+1 has more than k prime divisors).

%Y Cf. A074851, A140077, A140078, A140079 (complementary subsequences: m and m+1 have exactly k = 2, 3, 4, 5 prime divisors).

%K nonn

%O 1,1

%A _M. F. Hasler_, Nov 13 2018

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Last modified June 5 12:47 EDT 2020. Contains 334840 sequences. (Running on oeis4.)