OFFSET
0,4
COMMENTS
Sum of the primes in the n-th column of the example in A258087.
LINKS
Robert Israel, Table of n, a(n) for n = 0..10000
FORMULA
From Robert Israel, Jun 16 2017:
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)
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 *)
PROG
(PARI) a(n) = sum(i=floor((n-1)/2), n-1, i*isprime(i)) \\ Felix Fröhlich, Jun 16 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Jun 14 2017
STATUS
approved