A064009 a(n) = Sum_{k=1..n} d(k)*prime(k), where d(k) = A001223.

2, 8, 18, 46, 68, 120, 154, 230, 368, 426, 612, 760, 842, 1014, 1296, 1614, 1732, 2098, 2366, 2508, 2946, 3262, 3760, 4472, 4860, 5062, 5474, 5688, 6124, 7706, 8214, 9000, 9274, 10664, 10962, 11868, 12810, 13462, 14464, 15502, 15860, 17670, 18052

Offset: 1

Author

Jason Earls, Sep 06 2001

Keywords

• nonn

Examples

			a(4) = 2*(3-2) + 3*(5-3) + 5*(7-5) + 7*(11-7) = 46.
		

Links

• Harry J. Smith, Table of n, a(n) for n=1..1000

Crossrefs

Cf. A001223.

Partial sums of A291463.

Programs

Mathematica

Accumulate@ Array[# (NextPrime@ # - #) &@ Prime@ # &, {43}] (* Michael De Vlieger, May 05 2016 *)

PARI

d(n) = prime(n+1)-prime(n); j=[]; for(n=1,150,j=concat(j,sum(k=1,n, prime(k)*d(k)))); j

PARI

d(n)= { prime(n + 1) - prime(n) }
{ a=0; for (n=1, 1000, write("b064009.txt", n, " ", a+=prime(n)*d(n)) ) } \\ Harry J. Smith, Sep 05 2009

Sage

p=primes_first_n(44); d=differences(p); v=[]; a=0
for k in range(len(d)):
   a+=p[k]*d[k]; v.append(a)
print(v)  # Giuseppe Coppoletta, May 05 2016