A262723 Products of three distinct primes that form an arithmetic progression.

105, 231, 627, 897, 935, 1581, 1729, 2465, 2967, 4123, 4301, 4715, 5487, 7685, 7881, 9717, 10707, 11339, 14993, 16377, 17353, 20213, 20915, 23779, 25327, 26331, 26765, 29341, 29607, 32021, 33335, 40587, 40807, 42911, 48635, 49321, 54739, 55581, 55637, 59563, 60297, 63017

Offset: 1

Author

Antonio Roldán, Sep 28 2015

Keywords

• nonn

Comments

This sequence is subsequence of A046389, A088595, A187073, A203614 and A229094.

Obviously, the most repeated prime divisor for values of a(n) is 3. - Altug Alkan, Sep 30 2015

These are numbers 3(2k + 3)(4k + 3) where 2k + 3 and 4k + 3 are prime, together with numbers p(p - 6d)(p + 6d) where p, p - 6d, and p + 6d are prime. - Charles R Greathouse IV, Mar 16 2018

Examples

			627 is in this sequence because 627=3*11*19, and 3, 11, 19 form an arithmetic progression (11-3 = 19-11).
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A046389, A088595, A187073, A203614, A229094.

Programs

Mathematica

Select[Range@ 64000, And[SquareFreeQ@ #, PrimeOmega@ # == 3, Subtract @@ Differences[First /@ FactorInteger@ #] == 0] &] (* Michael De Vlieger, Sep 30 2015 *)

PARI

for(i=2,10^5,if(issquarefree(i)&&omega(i)==3,f=factor(i);if(f[1, 1]+f[3, 1]==2*f[2,1],print1(i,", "))))

PARI

list(lim)=my(v=List()); lim\=1; forstep(d=6,sqrtint(lim\10),6, forprime(p=d+5, solve(x=sqrtn(lim,3),d*sqrtn(lim,3), x^3-d^2*x-lim)+.5, if(isprime(p-d) && isprime(p+d), listput(v, p*(p-d)*(p+d))))); forprime(p=5,(sqrt(24*lim+81)-27)/12+3.5, if(isprime(2*p-3), listput(v,p*(2*p-3)*3))); Set(v) \\ Charles R Greathouse IV, Mar 16 2018

Extensions

New name from Peter Munn, Aug 27 2022