A349214 a(n) = Sum_{k=1..n} k^c(k), where c is the prime characteristic (A010051).

1, 3, 6, 7, 12, 13, 20, 21, 22, 23, 34, 35, 48, 49, 50, 51, 68, 69, 88, 89, 90, 91, 114, 115, 116, 117, 118, 119, 148, 149, 180, 181, 182, 183, 184, 185, 222, 223, 224, 225, 266, 267, 310, 311, 312, 313, 360, 361, 362, 363, 364, 365, 418, 419, 420, 421, 422, 423, 482, 483, 544

Offset: 1

Author

Wesley Ivan Hurt, Nov 10 2021

Keywords

• nonn

Comments

For k in 1 <= k <= n, add k if k is prime, otherwise add 1. For example a(6) = 1 + 2 + 3 + 1 + 5 + 1 = 13.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Partial sums of A089026.

Cf. A010051, A034387, A062298.

Programs

Mathematica

a[n_] := Sum[k^Boole[PrimeQ[k]], {k, 1, n}]; Array[a, 60] (* Amiram Eldar, Nov 11 2021 *)

PARI

a(n) = sum(k=1, n, if (isprime(k), k, 1)); \\ Michel Marcus, Nov 11 2021

Python

from sympy import primerange
def A349214(n):
    p = list(primerange(2,n+1))
    return n-len(p)+sum(p) # Chai Wah Wu, Nov 11 2021

Formula

a(n) = A034387(n) + A062298(n). - Wesley Ivan Hurt, Nov 23 2021