A253913 Numbers of the form m^k + m, with m >= 0 and k > 1.

0, 2, 6, 10, 12, 18, 20, 30, 34, 42, 56, 66, 68, 72, 84, 90, 110, 130, 132, 156, 182, 210, 222, 240, 246, 258, 260, 272, 306, 342, 350, 380, 420, 462, 506, 514, 520, 552, 600, 630, 650, 702, 732, 738, 756, 812, 870, 930, 992, 1010, 1026, 1028, 1056, 1122, 1190, 1260, 1302

Offset: 1

Author

Alex Ratushnyak, Jan 18 2015

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A099225, A253914.

Programs

Maple

N:= 10000: # for terms <= N
S:= 0, 2:
for k from 2 to floor(log[2](N)) do
  for m from 2 do
    v := m^k+m; if v > N then break fi;
    S:= S, v;
od od:
sort(convert({S}, list)): # Robert Israel, Apr 28 2019, changed Jul 8 2021

Mathematica

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 *)

Python

def aupto(lim):
    xkx = set(x**k + x for k in range(2, lim.bit_length()) for x in range(int(lim**(1/k))+2))
    return sorted(filter(lambda t: t<=lim, xkx))
print(aupto(1500)) # Michael S. Branicky, Jul 08 2021

Extensions

Changed to include 0 and 2 by Robert Israel, Jul 08 2021