cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-1 of 1 results.

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

Original entry on oeis.org

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

Views

Author

M. F. Hasler, Feb 21 2009

Keywords

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).

Programs

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

Formula

a(n) = 2*A156778( pi(n)), where pi(n) = A000720(n)= PrimePi(n) = #{primes <= n}.
Showing 1-1 of 1 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.