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

1,1

Comments

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

References

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

Links

Table of n, a(n) for n=1..53.

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

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

Example

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

Crossrefs

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

Sequence in context: A212314 A136318 A242139 * A117771 A227853 A275240

Adjacent sequences: A216762 A216763 A216764 * A216766 A216767 A216768

Keyword

nonn,easy

Author

Jonathan Vos Post, Sep 15 2012

Status

approved