A305728 - OEIS

%I #19 Sep 08 2022 08:46:21

%S 27000,474552,1061208,5268024,10941048,14886936,32157432,49027896,

%T 84027672,152273304,197137368,222545016,279726264,311665752,555412248,

%U 714516984,835896888,1118386872,1280824056,1552836312,1651400568,2593941624,2732256792,3023464536,3666512088

%N Numbers of the form 216*p^3, where p is a Pythagorean prime (A002144).

%C No term can be written as x^2 + y^2 + z^9.

%H Colin Barker, <a href="/A305728/b305728.txt">Table of n, a(n) for n = 1..1000</a>

%H W. Jagy and I. Kaplansky, <a href="https://projecteuclid.org/euclid.em/1062621075">Sums of Squares, Cubes and Higher Powers</a>, Experimental Mathematics, vol. 4 (1995), p. 171 (see Theorem under Higher powers).

%p P := select(p -> isprime(p), [seq(n, n=5..1000, 4)]):

%p seq((6*p)^3, p in P); # _Peter Luschny_, Jun 22 2018

%t P = Select[Range[5, 300, 4], PrimeQ];

%t A305728 = (6P)^3 (* _Jean-François Alcover_, Jun 22 2018 *)

%o (Magma) [216*p^3: p in PrimesUpTo(300) | IsOne(p mod 4)];

%o (PARI) first(n) = my(res=List()); forprime(p=5, oo, if(p%4 == 1, listput(res,(6*p)^3); n--; if(n==0, return(res)))) \\ _David A. Corneth_, Jun 27 2018

%Y Cf. A002144, A016911, A080169.

%K nonn

%O 1,1

%A _Bruno Berselli_, Jun 22 2018