

A325204


Numbers k such that k*(k+1)*(k+2) has exactly 4 distinct prime factors.


3



5, 9, 10, 11, 12, 14, 15, 17, 18, 22, 23, 24, 25, 26, 27, 30, 31, 32, 36, 46, 47, 48, 52, 62, 71, 72, 79, 80, 81, 96, 106, 107, 126, 127, 162, 191, 192, 241, 242, 256, 382, 431, 486, 512, 576, 862, 1151, 1152, 2186, 2591, 2592, 2916, 4372, 8191, 8746, 131071, 131072, 139967, 472391, 524287, 786431, 995326, 995327
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OFFSET

1,1


COMMENTS

Contains 2^p1 for p in A107360 except 3.
Contains all members of A325255 except 2 and 4.
Contains k1 for k in A027856 except 4.
Contains k2 for k in A327240 except 6 and 8.  Ray Chandler, Sep 14 2019


LINKS

Ray Chandler, Table of n, a(n) for n = 1..178 (terms < 10^1000, first 114 terms from Robert Israel)
Ray Chandler, Mathematica code used to compute bfile.
Math StackExchange, Three consecutive numbers with exactly different four prime factors


EXAMPLE

a(3)=10 is in the sequence because 10*11*12 has four distinct prime factors: 2, 3, 5, 11.


MAPLE

select(t > nops(numtheory:factorset(t) union numtheory:factorset(t+1) union numtheory:factorset(t+2))=4, [$1..10^6]);


PROG

(PARI) select(k>4==omega(k*(k+1)*(k+2)), [1..10000]) \\ Andrew Howroyd, Sep 05 2019


CROSSREFS

Cf. A027856, A107360, A325255, A327240.
Sequence in context: A314583 A205712 A093711 * A163670 A187713 A101082
Adjacent sequences: A325201 A325202 A325203 * A325205 A325206 A325207


KEYWORD

nonn


AUTHOR

J. M. Bergot and Robert Israel, Sep 05 2019


STATUS

approved



