A033955 a(n) = sum of the remainders when the n-th prime is divided by primes up to the (n-1)-th prime.

0, 1, 3, 4, 8, 13, 18, 27, 29, 46, 56, 70, 74, 88, 98, 134, 147, 171, 200, 217, 252, 274, 309, 323, 348, 418, 448, 471, 522, 571, 629, 685, 739, 777, 793, 853, 954, 997, 1002, 1120, 1148, 1220, 1338, 1419, 1466, 1540, 1615, 1573, 1633, 1707, 1825, 1892, 1986

Offset: 1

Author

Armand Turpel (armandt(AT)unforgettable.com)

Keywords

• nonn
• easy

Comments

Row sums of A207409. - Bob Selcoe, Apr 14 2014

Examples

			a(5) = 8. The remainders when the fifth prime 11 is divided by 2, 3, 5, 7 are 1, 2, 1, 4, respectively and their sum = 8.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A067435, A067436, A024934, A207409.

Programs

Maple

P:= [seq(ithprime(i),i=1..200)]:
f:= proc(n) local j;  add(P[n] mod P[j],j=1..n-1) end proc:
map(f, [$1..200]); # Robert Israel, Dec 29 2020

Mathematica

a[n_] := Sum[Mod[Prime[n], Prime[i]], {i, 1, n-1}]
Table[Total[Mod[Prime[n],Prime[Range[n-1]]]],{n,60}] (* Harvey P. Dale, Mar 07 2018 *)

PARI

{for(n=1, 200, print1(sum(k=1, n, prime(n)%prime(k)), ", "))}

Python

from sympy import prime; {print(sum(prime(n)%prime(k) for k in range(1,n)), end =', ') for n in range(1,54)} # Ya-Ping Lu, May 05 2024

Formula

a(n) = Sum_{k=1..n-1} ( prime(n) mod prime(k) ).

Extensions

Edited by Dean Hickerson, Mar 02 2002