A158662 Sum of primes <= n if 1 is counted as a prime.

1, 3, 6, 6, 11, 11, 18, 18, 18, 18, 29, 29, 42, 42, 42, 42, 59, 59, 78, 78, 78, 78, 101, 101, 101, 101, 101, 101, 130, 130, 161, 161, 161, 161, 161, 161, 198, 198, 198, 198, 239, 239, 282, 282, 282, 282, 329, 329, 329, 329, 329, 329

Offset: 1

Author

Jaroslav Krizek, Mar 23 2009, Apr 12 2009

Keywords

• nonn

Comments

a(n) = A034387(n) + 1. a(p) - a(p-1) = p, for p = primes (A000040), a(c) - a(c-1) = 0, for c = composite numbers (A002808).

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A034387, A000040, A002808.

Programs

Mathematica

Module[{nn=60,c},c=Join[{1},Prime[Range[PrimePi[nn]]]];Table[Total[ Select[ c,#<=n&]],{n,nn}]] (* Harvey P. Dale, Jun 01 2014 *)
Accumulate[Join[{1},Table[If[PrimeQ[n],n,0],{n,60}]]] (* Harvey P. Dale, Feb 27 2017 *)