A208247 Numbers having exactly one partition into two prime powers.

2, 3, 119, 127, 163, 179, 191, 193, 217, 219, 221, 223, 239, 251, 269, 311, 337, 343, 389, 403, 415, 419, 427, 431, 457, 491, 505, 547, 557, 569, 575, 581, 583, 597, 599, 613, 653, 659, 667, 671, 673, 683, 697, 719, 739, 749, 767, 779, 787, 799, 807, 817

Offset: 1

Author

Reinhard Zumkeller, Jan 11 2013

Keywords

• nonn

Comments

A071330(a(n)) = 1.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

A095841 = Intersection of A208247 and A000961.

Programs

Haskell

a095841 n = a095841_list !! (n-1)
a095841_list = filter ((== 1) . a071330) a000961_list

PARI

is(n)=sum(i=2,n\2,isprimepower(i)&&isprimepower(n-i))+isprimepower(n-1)==1 || n==2 \\ naive; Charles R Greathouse IV, Nov 21 2014

PARI

is(n)=my(s); forprime(p=2,n\2,if(isprimepower(n-p) && s++>1, return(0))); for(e=2,log(n)\log(2), forprime(p=2, sqrtnint(n\2,e), if(isprimepower(n-p^e) && s++>1,return(0)))); s+(!!isprimepower(n-1))==1 || n==2 \\ faster; Charles R Greathouse IV, Nov 21 2014