A024925 Sum of remainders of n mod prime(k), for k = 1,2,3,...,n.

1, 2, 4, 9, 13, 19, 25, 38, 52, 64, 74, 92, 104, 122, 143, 172, 188, 218, 236, 268, 299, 329, 351, 393, 437, 473, 523, 569, 597, 646, 676, 737, 788, 836, 893, 959, 995, 1049, 1110, 1182, 1222, 1293, 1335, 1409, 1490, 1556, 1602, 1692, 1782, 1874, 1955, 2043, 2095, 2197, 2290

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Crossrefs

Cf. A004125, A024934.

Programs

Magma

[&+[n mod NthPrime(k): k in [1..n]]:n in [1..55]]; // Marius A. Burtea, Jul 16 2019

PARI

a(n) = sum(k=1, n, n % prime(k)); \\ Michel Marcus, Jul 18 2019

PARI

a(n) = my(s=0); forprime(p=2, prime(n), s += n%p); s; \\ Michel Marcus, Jul 18 2019

Formula

G.f.: x * (1 + x)/(1 - x)^3 - (1/(1 - x)) * Sum_{k>=1} prime(k) * x^prime(k)/(1 - x^prime(k)). - Ilya Gutkovskiy, Jul 16 2019