A075424 -id:A075424 - cp's OEIS frontend

A075423 rad(n) - 1, where rad(n) is the squarefree kernel of n (A007947).

0, 1, 2, 1, 4, 5, 6, 1, 2, 9, 10, 5, 12, 13, 14, 1, 16, 5, 18, 9, 20, 21, 22, 5, 4, 25, 2, 13, 28, 29, 30, 1, 32, 33, 34, 5, 36, 37, 38, 9, 40, 41, 42, 21, 14, 45, 46, 5, 6, 9, 50, 25, 52, 5, 54, 13, 56, 57, 58, 29, 60, 61, 20, 1, 64, 65, 66, 33, 68, 69, 70, 5, 72, 73, 14, 37, 76, 77

Offset: 1

Reinhard Zumkeller, Sep 15 2002

nonn

a(n) < n for all n, see A075425.

A075424(n) = a(a(n)) for n>1.

a(n)=factorback(factor(n)[,1])-1 \\ Charles R Greathouse IV, Jul 09 2013

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

Original entry on oeis.org

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

Gleb Ivanov, Jan 10 2022

nonn

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

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

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 *)

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

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)])

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

cp's OEIS Frontend

A075423 rad(n) - 1, where rad(n) is the squarefree kernel of n (A007947).

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

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