A095842 Prime powers having no partition into two prime powers.

1, 149, 331, 373, 509, 701, 757, 809, 877, 907, 997, 1019, 1087, 1259, 1549, 1597, 1619, 1657, 1759, 1777, 1783, 1867, 1973, 2293, 2377, 2503, 2579, 2683, 2789, 2843, 2879, 2909, 2999, 3119, 3163, 3181, 3187, 3299, 3343, 3433, 3539, 3643

Offset: 1

Author

Reinhard Zumkeller, Jun 10 2004

Keywords

• nonn

Comments

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

A071330(a(n)) = 0.

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

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Crossrefs

Subsequence of A071331.

Cf. A000961, A095841.

Programs

Haskell

a095842 n = a095842_list !! (n-1)
a095842_list = filter ((== 0) . a071330) a000961_list
-- Reinhard Zumkeller, Jan 11 2013

PARI

isprimepower(n)=ispower(n,,&n);isprime(n)||n==1;
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)
\\ Charles R Greathouse IV, Jul 06 2011