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

1,2

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

Prog

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

Crossrefs

Subsequence of A071331.

Cf. A000961, A095841.

Sequence in context: A244661 A146137 A071331 * A142359 A185692 A216312

Adjacent sequences: A095839 A095840 A095841 * A095843 A095844 A095845

Keyword

nonn

Author

Reinhard Zumkeller, Jun 10 2004

Status

approved