A210469 a(n) = n - primepi(2n).
0, 0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 4, 5, 5, 5, 6, 7, 7, 8, 8, 8, 9, 9, 10, 11, 11, 12, 13, 13, 13, 14, 15, 15, 16, 16, 16, 17, 18, 18, 19, 19, 20, 21, 21, 22, 23, 24, 24, 25, 25, 25, 26, 26, 26, 27, 27, 28, 29, 30, 31, 32, 33, 33, 34, 34, 35, 36, 36, 36
Offset: 1
Examples
a(6) = 1 since 9 is the only odd composite number appearing in the partitions of 2*6 = 12 into two parts. For example, 12 = (1+11) = (2+10) = (3+9) = (4+8) = (5+7) = (6+6). Note that the numbers in the partitions with identical parts are counted only once.
Links
Programs
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Maple
with(numtheory); a:=n->n-pi(2*n); seq(a(k), k=1..70);
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Mathematica
Table[n - PrimePi[2 n], {n, 70}] (* Robert G. Wilson v, Jan 24 2013 *) -
PARI
a(n) = n - primepi(2*n); \\ Michel Marcus, Aug 05 2023
Formula
a(n) = n - primepi(2n).
Comments