A350661 a(1) = 1; a(n) = a(A007947(n) - 1) + n.

1, 3, 6, 5, 10, 16, 23, 9, 12, 22, 33, 22, 35, 49, 64, 17, 34, 28, 47, 32, 53, 75, 98, 34, 30, 56, 30, 63, 92, 122, 153, 33, 66, 100, 135, 46, 83, 121, 160, 52, 93, 135, 178, 97, 94, 140, 187, 58, 65, 62, 113, 82, 135, 64, 119, 91, 148, 206, 265, 152, 213, 275, 95, 65

Offset: 1

Author

Gleb Ivanov, Jan 10 2022

Keywords

• nonn

Examples

			a(3) = a(2) + 3 = a(1) + 5 = 6;
a(6) = a(5) + 6 = a(4) + 11 = a(1) + 15 = 16.
		

Crossrefs

Cf. A007947, A075423, A075425, A075424, A005187.

Programs

Mathematica

rad[n_] := Times @@ First /@ FactorInteger[n]; a[1] = 1; a[n_] := a[n] = a[rad[n] - 1] + n; Array[a, 100] (* Amiram Eldar, Jan 10 2022 *)

PARI

rad(n) = factorback(factorint(n)[, 1]); \\ A007947
a(n) = if (n==1, 1, a(rad(n) - 1) + n); \\ Michel Marcus, Jan 10 2022

Python

from sympy import prod, primefactors
from functools import lru_cache
rad = lambda n: prod(primefactors(n))
@lru_cache()
def a(n):
    if n == 1: return 1
    return a(rad(n)-1)+n
print([a(i) for i in range(1, 100)])

Formula

a(1) = 1; a(n) = a(A075423(n)) + n.