A253913 - OEIS

%I #19 Jul 10 2021 04:35:11

%S 0,2,6,10,12,18,20,30,34,42,56,66,68,72,84,90,110,130,132,156,182,210,

%T 222,240,246,258,260,272,306,342,350,380,420,462,506,514,520,552,600,

%U 630,650,702,732,738,756,812,870,930,992,1010,1026,1028,1056,1122,1190,1260,1302

%N Numbers of the form m^k + m, with m >= 0 and k > 1.

%H Robert Israel, <a href="/A253913/b253913.txt">Table of n, a(n) for n = 1..10000</a>

%p N:= 10000: # for terms <= N

%p S:= 0, 2:

%p for k from 2 to floor(log[2](N)) do

%p   for m from 2 do

%p     v := m^k+m; if v > N then break fi;

%p     S:= S, v;

%p od od:

%p sort(convert({S}, list)): # _Robert Israel_, Apr 28 2019, changed Jul 8 2021

%t max = 1000; Sort[Flatten[Table[m^k + m, {m, 2, Floor[Sqrt[max]]}, {k, 2, Floor[Log[m, max]]}]]] (* _Alonso del Arte_, Jan 18 2015 *)

%o (Python)

%o def aupto(lim):

%o     xkx = set(x**k + x for k in range(2, lim.bit_length()) for x in range(int(lim**(1/k))+2))

%o     return sorted(filter(lambda t: t<=lim, xkx))

%o print(aupto(1500)) # _Michael S. Branicky_, Jul 08 2021

%Y Cf. A099225, A253914.

%K nonn

%O 1,2

%A _Alex Ratushnyak_, Jan 18 2015

%E Changed to include 0 and 2 by _Robert Israel_, Jul 08 2021