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 A071330 Number of decompositions of n into sum of two prime powers. 11
 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 is a prime power then 149-x is 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-François Alcover, Nov 17 2011, after Michael B. 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, A010055, A061358, A071331, A109829. Sequence in context: A129843 A050430 A277329 * A092333 A107452 A205018 Adjacent sequences:  A071327 A071328 A071329 * A071331 A071332 A071333 KEYWORD nonn,nice AUTHOR Reinhard Zumkeller, May 19 2002 STATUS approved

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Last modified May 28 01:09 EDT 2018. Contains 304726 sequences. (Running on oeis4.)