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

1,2

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

Formula

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

Mathematica

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

Prog

(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

Crossrefs

Partial sums of A089026.

Cf. A010051, A034387, A062298.

Sequence in context: A032849 A038591 A333794 * A182181 A138038 A095029

Adjacent sequences: A349211 A349212 A349213 * A349215 A349216 A349217

Keyword

nonn

Author

Wesley Ivan Hurt, Nov 10 2021

Status

approved