A161226 - OEIS

%I #12 Sep 08 2022 08:45:45

%S 0,1,4,8,16,25,32,49,64,81,100,121,144,169,196,216,243,289,324,343,

%T 400,441,484,512,576,625,676,729,784,841,900,961,1000,1089,1156,1225,

%U 1296,1369,1444,1521,1600,1681,1728,1849,1936,2025,2116,2187,2304,2401,2500

%N a(0)=0. a(n) = the smallest integer of the form k^j, j>=2, such that a(n) >= a(n-1) + n.

%t fQ[n_] := GCD @@ Last /@ FactorInteger@n > 1; f[n_] := f[n] = Block[{k = f[n - 1] + n}, While[ !fQ@k, k++ ]; k]; f[0] = 0; f[1] = 1; Table[ f@n, {n, 0, 50}] (* _Robert G. Wilson v_, Jun 09 2009 *)

%o (Magma) P:=[1] cat [ n: n in [2..2500] | IsPower(n) ]; S:=[0]; p:=1; n:=1; while p le #P do if P[p] ge (S[ #S]+n) then Append(~S, P[p]); n+:=1; end if; p+:=1; end while; S; // _Klaus Brockhaus_, Jun 10 2009

%Y Cf. A001597.

%Y Cf. A001597 (perfect powers: m^k where m is an integer and k >= 2). - _Klaus Brockhaus_, Jun 10 2009

%K nonn

%O 0,3

%A _Leroy Quet_, Jun 06 2009

%E Extended by _Ray Chandler_, _Klaus Brockhaus_ and _Robert G. Wilson v_, Jun 11 2009