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A339276
Nearest integer to the fourth root of n.
1
1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3
OFFSET
1,6
LINKS
Jonathan M. Borwein and others, Nearest Integer Zeta Functions, solution to Problem 10212, The American Mathematical Monthly, Vol. 101, No. 6 (1994), pp. 579-580.
FORMULA
Sum_{n>=1} 1/a(n)^s = 4*zeta(s-3) + zeta(s-1), for s>4 (Borwein, 1994).
EXAMPLE
a(1) = 1 since 1^(1/4) = 1.
a(6) = 2 since 6^(1/4) = 1.565... and its nearest integer is 2.
MATHEMATICA
Table[Round[Surd[n, 4]], {n, 1, 100}]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Dec 13 2020
STATUS
approved