A325204 Numbers k such that k*(k+1)*(k+2) has exactly 4 distinct prime factors.

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

Offset

1,1

Comments

Contains 2^p-1 for p in A107360 except 3.

Contains all terms of A325255 except 2 and 4.

Contains k-1 for k in A027856 except 4.

Contains k-2 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 b-file.

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