A099850 Partial sums of A004648.

0, 1, 3, 6, 7, 8, 11, 14, 19, 28, 37, 38, 40, 41, 43, 48, 56, 63, 73, 84, 94, 107, 121, 138, 160, 183, 205, 228, 250, 273, 276, 279, 284, 287, 296, 303, 312, 323, 334, 347, 362, 375, 394, 411, 428, 443, 466, 497, 528, 557, 586, 617, 646, 681, 718, 757, 798, 837

Offset: 1

Author

Mark Hudson (mrmarkhudson(AT)hotmail.com), Oct 27 2004

Keywords

• easy
• nonn

Examples

			A004648 begins: 0, 1, 2, 3, 1, 1, 3, 3, 5, 9, 9, ... so the partial sums are 0, 1, 3, 6, 7, 8, 11, 14, 19, 28, 37, ...
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A004648.

Programs

Magma

[(&+[(NthPrime(k) mod k): k in [1..n]]): n in [1..100]]; // G. C. Greubel, Apr 20 2023

Mathematica

Table[Sum[Mod[Prime[j], j], {j,n}], {n,100}] (* G. C. Greubel, Apr 20 2023 *)
Accumulate[Table[Mod[Prime[n],n],{n,100}]] (* Harvey P. Dale, Jun 14 2023 *)

PARI

s=vector(100):s[1]=prime(1)%1:for(n=2,100,s[n]=s[n-1]+prime(n)%n)

SageMath

def A004648(n): return (nth_prime(n)%n)
def A099850(n): return sum(A004648(k) for k in range(1,n+1))
[A099850(n) for n in range(1,101)] # G. C. Greubel, Apr 20 2023

Formula

a(n) = Sum_{k=1..n} A004648(k).