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A196228 Number of ways of writing n as sum of a prime and a perfect power. 3
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 (list; graph; refs; listen; history; text; internal format)
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: A135063 A124010 A212171 * A133364 A063420 A254631

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

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Last modified October 22 20:57 EDT 2018. Contains 316502 sequences. (Running on oeis4.)