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A060303
Number of primes below n^2 does not exceed n times the number of primes below n.
1
0, 0, 2, 2, 6, 7, 13, 14, 14, 15, 25, 26, 39, 40, 42, 42, 58, 60, 80, 82, 83, 84, 108, 111, 111, 112, 114, 115, 144, 146, 179, 180, 182, 183, 185, 186, 225, 228, 228, 229, 270, 272, 319, 321, 324, 325, 376, 378, 378, 383, 387, 387, 439, 443, 446, 451, 455, 454
OFFSET
1,3
LINKS
Sanford L. Segal, On Pi(x+y)<=Pi(x)+Pi(y), Transactions American Mathematical Society, Vol. 104, No. 3 (1962), pp. 523-527.
FORMULA
Table[n*PrimePi[n]-PrimePi[n^2], {n, 1, 100}]
EXAMPLE
pi(100) = 25, 10*pi(10) = 40, a(10) = 40-25 = 15.
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Mar 26 2001
EXTENSIONS
Offset corrected by Amiram Eldar, Sep 06 2024
STATUS
approved