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A071330 Number of decompositions of n into sum of two prime powers. 8
0, 1, 1, 2, 2, 3, 2, 3, 3, 4, 3, 4, 3, 4, 3, 4, 3, 5, 3, 5, 4, 4, 2, 5, 3, 5, 4, 5, 3, 6, 3, 7, 5, 7, 4, 7, 2, 6, 4, 6, 3, 6, 3, 6, 5, 6, 2, 8, 3, 8, 4, 6, 2, 9, 3, 7, 4, 6, 2, 8, 3, 7, 4, 7, 3, 9, 2, 8, 5, 7, 2, 10, 3, 8, 6, 7, 3, 9, 2, 9, 4, 7, 4, 11, 3, 9, 4, 7, 3, 12, 4, 8, 3, 7, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

a(2*n) > 0 (Goldbach's conjecture).

a(A071331(n)) = 0; A095840(n) = a(A000961(n)).

LINKS

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

EXAMPLE

10 = 1+3^2 = 2+2^3 = 3+7 = 5+5, therefore a(10) = 4;

11 = 2+3^2 = 3+2^3 = 4+7, therefore a(11) = 3;

12 = 1+11 = 3+3^2 = 2^2+2^3 = 5+7, therefore a(12) = 4;

a(149)=0, as for all x<149: if x prime power then 149-x not.

MATHEMATICA

primePowerQ[n_] := Length[ FactorInteger[n]] == 1; a[n_] := (r = 0; Do[ If[ primePowerQ[k] && primePowerQ[n-k], r++], {k, 1, Floor[n/2]}]; r); Table[a[n], {n, 1, 95}](* Jean-Fran├žois Alcover, Nov 17 2011, after Michael Porter *)

PROG

(PARI) ispp(n) = (omega(n)==1 || n==1)

A071330(n) = {local(r); r=0; for(i=1, floor(n/2), if(ispp(i) && ispp(n-i), r++)); r} \\ Michael B. Porter, Dec 04 2009

(PARI) a(n)=my(s); forprime(p=2, n\2, if(isprimepower(n-p), s++)); for(e=2, log(n)\log(2), forprime(p=2, sqrtnint(n\2, e), if(isprimepower(n-p^e), s++))); s+(!!isprimepower(n-1))+(n==2) \\ Charles R Greathouse IV, Nov 21 2014

(Haskell)

a071330 n = sum $

   map (a010055 . (n -)) $ takeWhile (<= n `div` 2) a000961_list

-- Reinhard Zumkeller, Jan 11 2013

CROSSREFS

Cf. A000961, A002375, A071331, A061358, A109829, A010055.

Sequence in context: A182745 A129843 A050430 * A092333 A107452 A205018

Adjacent sequences:  A071327 A071328 A071329 * A071331 A071332 A071333

KEYWORD

nonn,nice,changed

AUTHOR

Reinhard Zumkeller, May 19 2002

STATUS

approved

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Last modified November 23 01:23 EST 2014. Contains 249836 sequences.