A383438 a(n) = Sum_{k=1..n} Product_{p|k, p prime} k/p.

1, 2, 3, 5, 6, 12, 13, 17, 20, 30, 31, 55, 56, 70, 85, 93, 94, 148, 149, 189, 210, 232, 233, 329, 334, 360, 369, 425, 426, 1326, 1327, 1343, 1376, 1410, 1445, 1661, 1662, 1700, 1739, 1899, 1900, 3664, 3665, 3753, 3888, 3934, 3935, 4319, 4326, 4576, 4627, 4731

Offset: 1

Author

Peter Luschny, Apr 27 2025

Keywords

• nonn

Crossrefs

Cf. A205959.

Programs

Mathematica

a[n_]:=Sum[Product[k/p,{p,Select[Divisors[k],PrimeQ[#] &]}],{k,n}]; Array[a,52] (* Stefano Spezia, Apr 27 2025 *)

PARI

a(n) = sum(k=1, n, my(f=factor(k)[, 1]); prod(i=1, #f, k/f[i])); \\ Michel Marcus, Apr 27 2025

SageMath

from itertools import accumulate
def A383438List(len: int) -> list[int]:
    return list(accumulate([A205959(n) for n in range(1, len + 1)]))
print(A383438List(52))

Formula

a(n) = Sum_{k=1..n} A205959(k).