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A095842 Prime powers having no partition into two prime powers.

%I A095842 #16 Nov 28 2014 17:10:26
%S A095842 1,149,331,373,509,701,757,809,877,907,997,1019,1087,1259,1549,1597,
%T A095842 1619,1657,1759,1777,1783,1867,1973,2293,2377,2503,2579,2683,2789,
%U A095842 2843,2879,2909,2999,3119,3163,3181,3187,3299,3343,3433,3539,3643
%N A095842 Prime powers having no partition into two prime powers.
%C A095842 A095840(A095874(a(n))) = 0.
%C A095842 A071330(a(n)) = 0.
%C A095842 Here, "prime powers" is used in the relaxed sense, including 1. The numbers 96721, 121801, 192721, 205379, 226981,... seem to be the smallest composite terms of this sequence, which establishes the difference with the subsequence A115231. - _M. F. Hasler_, Nov 20 2014
%H A095842 Reinhard Zumkeller, <a href="/A095842/b095842.txt">Table of n, a(n) for n = 1..1000</a>
%o A095842 (PARI) isprimepower(n)=ispower(n,,&n);isprime(n)||n==1;
%o A095842 isA095842(n)=if(!isprimepower(n),return(0));forprime(p=2,n\2,if(isprimepower(n-p),return(0)));forprime(p=2,sqrtint(n\2),for(e=1,log(n\2)\log(p),if(isprimepower(n-p^e),return(0))));!isprimepower(n-1)
%o A095842 \\ _Charles R Greathouse IV_, Jul 06 2011
%o A095842 (Haskell)
%o A095842 a095842 n = a095842_list !! (n-1)
%o A095842 a095842_list = filter ((== 0) . a071330) a000961_list
%o A095842 -- _Reinhard Zumkeller_, Jan 11 2013
%Y A095842 Subsequence of A071331.
%Y A095842 Cf. A000961, A095841.
%K A095842 nonn
%O A095842 1,2
%A A095842 _Reinhard Zumkeller_, Jun 10 2004