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 A262723 Products of three distinct primes that form an arithmetic progression. 10
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 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 LINKS Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 EXAMPLE 627 is in this sequence because 627=3*11*19, and 3, 11, 19 form an arithmetic progression (11-3 = 19-11). MATHEMATICA Select[Range@ 64000, And[SquareFreeQ@ #, PrimeOmega@ # == 3, Subtract @@ Differences[First /@ FactorInteger@ #] == 0] &] (* Michael De Vlieger, Sep 30 2015 *) PROG (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 CROSSREFS Cf. A046389, A088595, A187073, A203614, A229094. Sequence in context: A308643 A229094 A307108 * A250757 A350199 A146257 Adjacent sequences: A262720 A262721 A262722 * A262724 A262725 A262726 KEYWORD nonn AUTHOR Antonio Roldán, Sep 28 2015 EXTENSIONS New name from Peter Munn, Aug 27 2022 STATUS approved

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Last modified June 3 13:22 EDT 2023. Contains 363110 sequences. (Running on oeis4.)