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A262723 Squarefree products of three primes whose prime divisors form an arithmetic progression. 6
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: A176878 A088595 A229094 * A250757 A146257 A075764

Adjacent sequences:  A262720 A262721 A262722 * A262724 A262725 A262726

KEYWORD

nonn

AUTHOR

Antonio Roldán, Sep 28 2015

STATUS

approved

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Last modified November 18 19:27 EST 2018. Contains 317324 sequences. (Running on oeis4.)