A196228 - OEIS

%I #27 Feb 18 2017 14:26:27

%S 0,0,1,1,0,2,1,1,1,1,3,2,1,2,2,1,1,2,2,2,3,1,2,1,1,1,4,2,2,3,1,4,2,2,

%T 3,1,2,5,4,2,2,2,2,3,4,2,3,2,3,2,4,2,2,3,3,4,2,1,2,2,2,4,3,1,2,3,3,5,

%U 4,2,2,3,2,2,5,1,4,2,3,4,2,1,5,3,1,4,4

%N Number of ways of writing n as sum of a prime and a perfect power.

%C In this case, perfect power does not include 0.

%C Different from A133364. The first difference is at n=74, where a(n) = 2 but A133364(n) = 3.

%H T. D. Noe, <a href="/A196228/b196228.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = Card_{n=i+j where i is in A000040 and j is in A001597}.

%F G.f.: (Sum_{k>=1} x^prime(k))*(Sum_{k = i^j, i>=1, j>=2} x^k). - _Ilya Gutkovskiy_, Feb 18 2017

%e a(1) = a(2) = a(5) = a(1549) = a(1771561) = 0, see A119748.

%t nn = 100; pwrs = Union[{1}, Flatten[Table[Range[2, Floor[nn^(1/ex)]]^ex, {ex, 2, Floor[Log[2, nn]]}]]]; pp = Prime[Range[PrimePi[nn]]]; t = Table[0, {nn}]; Do[ t[[i[[1]]]] = i[[2]], {i, Tally[Sort[Select[Flatten[Outer[Plus, pwrs, pp]], # <= nn &]]]}]; t (* _T. D. Noe_, Sep 29 2011 *)

%Y Cf. A119748 (zero terms).

%Y Cf. A000040, A001597, A133364.

%K easy,nonn

%O 1,6

%A _Philippe Deléham_, Sep 29 2011

%E Edited by _Franklin T. Adams-Watters_, Sep 29 2011