A156780 sp(n)*pi(n) = A034387(n)*A000720(n) = (sum of primes <= n)*(number of primes <= n).

0, 0, 2, 10, 10, 30, 30, 68, 68, 68, 68, 140, 140, 246, 246, 246, 246, 406, 406, 616, 616, 616, 616, 900, 900, 900, 900, 900, 900, 1290, 1290, 1760, 1760, 1760, 1760, 1760, 1760, 2364, 2364, 2364, 2364, 3094, 3094, 3934, 3934, 3934, 3934, 4920, 4920, 4920

Offset

0,3

Comments

All terms are even, since the parity of sp(n)=A034387(n) is always the opposite of pi(n)=A000720(n). Indeed, both change by an odd amount at each prime, starting with the first nonzero values sp(2)=2 and pi(2)=1. Thus one might also consider the integer sequence a(n)/2 = 0, 0, 1, 5, 5, 15, 15, 34, 34, 34, 34, 70, 70, 123, 123, 123, 123, 203, 203, 308,.... Sequence A156778 lists these values (without duplicates).

Links

Table of n, a(n) for n=0..49.

Formula

a(n) = 2*A156778( pi(n)), where pi(n) = A000720(n)= PrimePi(n) = #{primes <= n}.

Prog

(PARI) vector(80, n, sum(i=1, primepi(n), prime(i))*primepi(n))

Crossrefs

Sequence in context: A355486 A168381 A212621 * A206486 A067046 A066394

Adjacent sequences: A156777 A156778 A156779 * A156781 A156782 A156783

Keyword

nonn

Author

M. F. Hasler, Feb 21 2009

Status

approved