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

1,1

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.

Links

Table of n, a(n) for n=1..42.

Formula

A321504 \ A140078.

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 *)

Prog

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

Crossrefs

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

Sequence in context: A362217 A330427 A289824 * A252103 A074484 A186583

Adjacent sequences: A321491 A321492 A321493 * A321495 A321496 A321497

Keyword

nonn

Author

M. F. Hasler, Nov 12 2018

Status

approved