A321494 Numbers k such that k and k+1 have at least 4 but not both exactly 4 distinct prime factors.

38570, 40754, 51414, 51765, 58695, 60605, 62985, 66044, 68585, 70889, 71070, 73185, 73814, 74865, 77349, 82004, 83265, 83720, 83979, 85085, 87009, 90804, 90915, 91805, 91884, 92378, 94094, 94829, 96459, 97565, 98769, 98889, 100814, 101269, 101660, 104005, 104754, 105468, 107184, 108030, 108185, 108965

Offset: 1

Author

M. F. Hasler, Nov 12 2018

Keywords

• nonn

Comments

A321504 lists numbers n such that k and k+1 both have at least 4 distinct prime factors, while A140078 lists numbers such that k and k+1 have exactly 4 distinct prime factors. This sequence is the complement of the latter in the former, it consists of terms with indices (124, 214, 219, 276, 321, 415, ...) of the former.

Crossrefs

Cf. A140078, A321504; A321493, A321496 (analog for 3 & 5 factors).

Programs

Mathematica

aQ[n_]:=Module[{v={PrimeNu[n],PrimeNu[n+1]}},Min[v]>3 && v!={4,4}]; Select[Range[120000], aQ] (* Amiram Eldar, Nov 12 2018 *)

PARI

is(n)=vecmin(n=[omega(n),omega(n+1)])>=4&&n!=[4,4]

Formula

A321504 \ A140078.