A327240 -id:A327240 - 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

A325255 3-smooth numbers k such that k+1 and (k+2)/2 are prime.

Original entry on oeis.org

2, 4, 12, 36, 72, 192, 1152, 2592, 2916, 1492992, 1990656, 5308416, 28311552, 6879707136, 1761205026816, 5566277615616, 79164837199872, 3799912185593856, 115422332637413376, 1332669751402954752, 4803028329503971872

Offset: 1

Robert Israel, Sep 05 2019

nonn

Numbers k of the form 2^a*3^b such that k+1 and (k+2)/2 are prime.
All terms except 2 and 4 are in A325204.
All terms except 4 end in 2 or 6.

			a(3)=12 is a term because 12=2^2*3 and 13 and 14/2 are prime.

Ray Chandler, Table of n, a(n) for n = 1..41 (terms < 10^1000; first 39 terms from Robert Israel)

Cf. A003586, A325204, A327240.

N:= 10^100: # to get terms <= N
sort(select(t -> isprime(t+1) and isprime((t+2)/2), [seq(seq(2^i*3^j, i = 1 .. ilog2(N/3^j)), j=0..floor(log[3](N)))]));

cp's OEIS Frontend

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

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A325255 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

A325255 3-smooth numbers k such that k+1 and (k+2)/2 are prime.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

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