A061536 a(1) = 1 and a(n) = a(n-1) + (the number of primes <= n) for n > 1.

1, 2, 4, 6, 9, 12, 16, 20, 24, 28, 33, 38, 44, 50, 56, 62, 69, 76, 84, 92, 100, 108, 117, 126, 135, 144, 153, 162, 172, 182, 193, 204, 215, 226, 237, 248, 260, 272, 284, 296, 309, 322, 336, 350, 364, 378, 393, 408, 423, 438, 453, 468, 484, 500, 516, 532, 548

Offset: 1

Author

R. K. Guy, Robert G. Wilson v, May 14 2001

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A000720, A046992.

Programs

Mathematica

a[1] = 1; a[n_] := a[n - 1] + PrimePi[n]; Table[ a[n], {n, 1, 70} ]
Accumulate[PrimePi[Range[60]]]+1 (* Harvey P. Dale, Jun 11 2014 *)

PARI

a=1; for (n=1, 100, print1(a+=primepi(n), ", ")) \\ Harry J. Smith, Jul 24 2009

PARI

first(n)=my(p,s=1); vector(n,k, s+=p+=isprime(k)) \\ Charles R Greathouse IV, Jan 06 2016

Formula

a(n) = 1 + A046992(n).

Extensions

Definition edited by Georg Fischer, Sep 04 2020