A196228 Number of ways of writing n as sum of a prime and a perfect power.

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, 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, 4, 2, 2, 3, 2, 2, 5, 1, 4, 2, 3, 4, 2, 1, 5, 3, 1, 4, 4

Offset

1,6

Comments

In this case, perfect power does not include 0.

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

Links

T. D. Noe, Table of n, a(n) for n = 1..10000

Formula

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

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

Example

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

Mathematica

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 *)

Crossrefs

Cf. A119748 (zero terms).

Cf. A000040, A001597, A133364.

Sequence in context: A212171 A337255 A337375 * A133364 A063420 A347917

Adjacent sequences: A196225 A196226 A196227 * A196229 A196230 A196231

Keyword

easy,nonn

Author

Philippe Deléham, Sep 29 2011

Extensions

Edited by Franklin T. Adams-Watters, Sep 29 2011

Status

approved