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A262723
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Products of three distinct primes that form an arithmetic progression.
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10
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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
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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EXAMPLE
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627 is in this sequence because 627=3*11*19, and 3, 11, 19 form an arithmetic progression (11-3 = 19-11).
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MATHEMATICA
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Select[Range@ 64000, And[SquareFreeQ@ #, PrimeOmega@ # == 3, Subtract @@ Differences[First /@ FactorInteger@ #] == 0] &] (* Michael De Vlieger, Sep 30 2015 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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