A288726 a(n) = Sum_{i=floor((n-1)/2)..n-1} i * c(i), where c is the prime characteristic (A010051).
0, 0, 0, 2, 5, 5, 10, 8, 15, 12, 12, 12, 23, 18, 31, 31, 31, 24, 41, 41, 60, 60, 60, 60, 83, 72, 72, 72, 72, 59, 88, 88, 119, 119, 119, 119, 119, 102, 139, 139, 139, 120, 161, 161, 204, 204, 204, 204, 251, 228, 228, 228, 228, 228, 281, 281, 281, 281, 281, 281, 340, 311, 372, 372, 372, 341, 341, 341, 408
Offset: 0
Links
- Robert Israel, Table of n, a(n) for n = 0..10000
Programs
-
Maple
with(numtheory): A288726:=n->add(i*(pi(i)-pi(i-1)), i=floor((n-1)/2)..n-1): seq(A288726(n), n=0..100); # Alternative: M:= 100: # to get a(0) to a(2*M+1) A:= Array(0..2*M+1): A[3]:= 2: for k from 2 to M do if isprime(2*k-1) then A[2*k]:= A[2*k-1]+2*k-1 else A[2*k]:=A[2*k-1] fi; if isprime(k-1) then A[2*k+1]:= A[2*k]-(k-1) else A[2*k+1]:= A[2*k] fi; od: convert(A,list); # Robert Israel, Jun 16 2017
-
Mathematica
Table[Sum[i (PrimePi[i] - PrimePi[i - 1]), {i, Floor[(n - 1)/2], n - 1}], {n, 0, 68}] (* Michael De Vlieger, Jun 14 2017 *) -
PARI
a(n) = sum(i=floor((n-1)/2), n-1, i*isprime(i)) \\ Felix Fröhlich, Jun 16 2017
Formula
From Robert Israel, Jun 16 2017: (Start)
For k >= 2, a(2*k+1) - a(2*k) = 1-k if k-1 is prime, otherwise 0.
a(2*k+2) - a(2*k+1) = 2*k+1 if 2*k+1 is prime, otherwise 0. (End)
Comments