

A321494


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


7



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
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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: A050766 A250712 A289824 * A252103 A074484 A186583
Adjacent sequences: A321491 A321492 A321493 * A321495 A321496 A321497


KEYWORD

nonn


AUTHOR

M. F. Hasler, Nov 12 2018


STATUS

approved



