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A216765
Perfect powers (squares, cubes, etc.) plus 1.
22
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
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
KEYWORD
nonn,easy
AUTHOR
Jonathan Vos Post, Sep 15 2012
STATUS
approved