A216765 - OEIS

%I #21 Oct 15 2020 04:44:50

%S 5,9,10,17,26,28,33,37,50,65,82,101,122,126,129,145,170,197,217,226,

%T 244,257,290,325,344,362,401,442,485,513,530,577,626,677,730,785,842,

%U 901,962,1001,1025,1090,1157,1226,1297,1332,1370,1445,1522,1601,1682,1729,1765

%N Perfect powers (squares, cubes, etc.) plus 1.

%C Integers of the form m^k + 1 for integers m, k >= 2.

%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.6, p. 113.

%H Vsevolod F. Lev, <a href="https://listserv.nodak.edu/cgi-bin/wa.exe?A2=NMBRTHRY;fae68ff5.0205">Re: The sequence of 'perfect' powers</a>, Number Theory List, May 21, 2002.

%F a(n) = A001597(n+1) + 1 = A045542(n) + 2. [corrected by _Georg Fischer_, Jun 21 2020]

%F Sum_{n>=1} 1/a(n) = Pi^2/3 - 5/2 (Lev, 2002). - _Amiram Eldar_, Oct 15 2020

%e a(1) = 2^2 + 1; a(2) = 2^3 + 1; a(3) = 3^2 + 1; a(4) = 2^4 + 1.

%Y Cf. A001597, A045542, A175064, A195055, A214390, A214391.

%K nonn,easy

%O 1,1

%A _Jonathan Vos Post_, Sep 15 2012