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

%I A350661 #19 Feb 19 2022 14:23:50
%S A350661 1,3,6,5,10,16,23,9,12,22,33,22,35,49,64,17,34,28,47,32,53,75,98,34,
%T A350661 30,56,30,63,92,122,153,33,66,100,135,46,83,121,160,52,93,135,178,97,
%U A350661 94,140,187,58,65,62,113,82,135,64,119,91,148,206,265,152,213,275,95,65
%N A350661 a(1) = 1; a(n) = a(A007947(n) - 1) + n.
%F A350661 a(1) = 1; a(n) = a(A075423(n)) + n.
%e A350661 a(3) = a(2) + 3 = a(1) + 5 = 6;
%e A350661 a(6) = a(5) + 6 = a(4) + 11 = a(1) + 15 = 16.
%t A350661 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 *)
%o A350661 (Python)
%o A350661 from sympy import prod, primefactors
%o A350661 from functools import lru_cache
%o A350661 rad = lambda n: prod(primefactors(n))
%o A350661 @lru_cache()
%o A350661 def a(n):
%o A350661     if n == 1: return 1
%o A350661     return a(rad(n)-1)+n
%o A350661 print([a(i) for i in range(1, 100)])
%o A350661 (PARI) rad(n) = factorback(factorint(n)[, 1]); \\ A007947
%o A350661 a(n) = if (n==1, 1, a(rad(n) - 1) + n); \\ _Michel Marcus_, Jan 10 2022
%Y A350661 Cf. A007947, A075423, A075425, A075424, A005187.
%K A350661 nonn
%O A350661 1,2
%A A350661 _Gleb Ivanov_, Jan 10 2022