A216765 Perfect powers (squares, cubes, etc.) plus 1.

5, 9, 10, 17, 26, 28, 33, 37, 50, 65, 82, 101, 122, 126, 129, 145, 170, 197, 217, 226, 244, 257, 290, 325, 344, 362, 401, 442, 485, 513, 530, 577, 626, 677, 730, 785, 842, 901, 962, 1001, 1025, 1090, 1157, 1226, 1297, 1332, 1370, 1445, 1522, 1601, 1682, 1729, 1765

Offset: 1

Author

Jonathan Vos Post, Sep 15 2012

Keywords

• nonn
• easy

Comments

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

Examples

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

References

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

Links

• Vsevolod F. Lev, Re: The sequence of 'perfect' powers, Number Theory List, May 21, 2002.

Crossrefs

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

Formula

a(n) = A001597(n+1) + 1 = A045542(n) + 2. [corrected by Georg Fischer, Jun 21 2020]

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