A185379 - OEIS

A185379

Product of exactly three distinct primes congruent to 1 mod 8 (A007519).

50881, 62033, 67609, 78761, 95489, 110449, 120377, 134521, 140233, 146761, 162401, 167977, 170017, 170969, 179129, 186337, 195857, 207281, 218161, 225913, 234889, 239513, 246041, 263177, 266377, 279497, 285073, 289153, 290321, 292009, 299081, 301801, 312953

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OFFSET

1,1

COMMENTS

Subset of numbers that are divisible by exactly 3 primes (counted with multiplicity), also known as triprimes or 3-almost primes, A014612. Subset of {d = p_1 * p_2 * ... * p_m where p_i == 1 (mod 8), 1 <= i <= m are distinct primes} as occurs in Wei, p.2.

LINKS

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

Dasheng Wei, On the equation x^2-Dy^2=n, Feb 18, 2011.

FORMULA

{A007519(i) * A007519(j) * A007519(k) for i < j < k}. {A000040(i) * A000040(j) * A000040(k) for i < j < k, and A000040(i) in A017077 and A000040(j) in A017077 and A000040(k) in A017077}.

EXAMPLE

a(12) = 170017 = 17 * 73 * 137 = A007519(1) * A007519(3) * A007519(7).

MATHEMATICA

p = Select[Prime[Range[100]], Mod[#, 8] == 1 &]; Sort[Reap[Do[n = p[[i]] p[[j]] p[[k]]; If[n <= p[[1]] p[[2]] p[[-1]], Sow[n]], {i, 2, Length[p]}, {j, i - 1}, {k, j - 1}]][[2, 1]]]

PROG

(PARI) list(lim)=my(v=List(), u=v, t); forprime(p=2, lim\697, if(p%8==1, listput(u, p))); for(i=1, #u-2, for(j=i+1, #u-1, if(u[i]*u[j]*u[j+1]>lim, break); for(k=j+1, #u, t=u[i]*u[j]*u[k]; if(t>lim, break); listput(v, t)))); Set(v) \\ Charles R Greathouse IV, Jan 31 2017

CROSSREFS

Cf. A007519, A014612, A017077, A185377.

Sequence in context: A233977 A282336 A043672 * A204729 A277344 A209846

Adjacent sequences: A185376 A185377 A185378 * A185380 A185381 A185382

KEYWORD

nonn,easy

AUTHOR

Jonathan Vos Post, Feb 20 2011

STATUS

approved