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Prime powers having no partition into two prime powers.
5

%I #16 Nov 28 2014 17:10:26

%S 1,149,331,373,509,701,757,809,877,907,997,1019,1087,1259,1549,1597,

%T 1619,1657,1759,1777,1783,1867,1973,2293,2377,2503,2579,2683,2789,

%U 2843,2879,2909,2999,3119,3163,3181,3187,3299,3343,3433,3539,3643

%N Prime powers having no partition into two prime powers.

%C A095840(A095874(a(n))) = 0.

%C A071330(a(n)) = 0.

%C 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 Reinhard Zumkeller, <a href="/A095842/b095842.txt">Table of n, a(n) for n = 1..1000</a>

%o (PARI) isprimepower(n)=ispower(n,,&n);isprime(n)||n==1;

%o 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 \\ _Charles R Greathouse IV_, Jul 06 2011

%o (Haskell)

%o a095842 n = a095842_list !! (n-1)

%o a095842_list = filter ((== 0) . a071330) a000961_list

%o -- _Reinhard Zumkeller_, Jan 11 2013

%Y Subsequence of A071331.

%Y Cf. A000961, A095841.

%K nonn

%O 1,2

%A _Reinhard Zumkeller_, Jun 10 2004