A325255 -id:A325255 - cp's OEIS frontend

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

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

nonn

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

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

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.

Cf. A027856, A107360, A325255, A327240.

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

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

A327240 3-smooth numbers k such that k-1 and (k-2)/2 are prime.

Original entry on oeis.org

6, 8, 12, 24, 48, 108, 384, 864, 8748, 995328, 2348273369088, 7421703487488, 21422803359744, 3470494144278528, 161919374795459002368, 1838129271989302091317248, 2168345519443636233418208968704, 28070062609828769223367060340342784

Offset: 1

Ray Chandler, Sep 14 2019

nonn

Numbers k of the form 2^a*3^b such that k-1 and (k-2)/2 are prime.
For all terms k except 6 and 8, k-2 is in A325204.
All terms except 6 and 12 end in 4 or 8.

			a(3)=12 is a term because 12=2^2*3 and 11 and 10/2 are prime.

Ray Chandler, Table of n, a(n) for n = 1..39 (terms < 10^1000)

Cf. A003586, A325204, A325255.

nmax = 10^35;
Select[Sort[Flatten[Table[2^i*3^j, {j, 0, Log[3, nmax]}, {i, Log[2, nmax/3^j]}]]], PrimeQ[# - 1] && PrimeQ[(# - 2)/2] &]

cp's OEIS Frontend

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

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A327240 3-smooth numbers k such that k-1 and (k-2)/2 are prime.

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cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

PARI

A327240 3-smooth numbers k such that k-1 and (k-2)/2 are prime.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

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