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A348623 a(1) = 1; for n > 1 a(n) = a(n-1) + A001227(a(n-1)).

%I A348623 #24 Dec 14 2021 01:43:46
%S A348623 1,2,3,5,7,9,12,14,16,17,19,21,25,28,30,34,36,39,43,45,51,55,59,61,63,
%T A348623 69,73,75,81,86,88,90,96,98,101,103,105,113,115,119,123,127,129,133,
%U A348623 137,139,141,145,149,151,153,159,163,165,173,175,181,183,187,191,193,195,203
%N A348623 a(1) = 1; for n > 1 a(n) = a(n-1) + A001227(a(n-1)).
%t A348623 NestList[# + Count[Divisors[#], _?OddQ] &, 1, 62] (* _Michael De Vlieger_, Oct 25 2021 *)
%o A348623 (PARI) f(n) = sumdiv(n, d, d%2); \\ A001227
%o A348623 a(n) = if (n==1, 1, my(x=a(n-1)); x + f(x)); \\ _Michel Marcus_, Oct 26 2021
%o A348623 (Python)
%o A348623 from math import prod
%o A348623 from itertools import islice
%o A348623 from sympy import factorint
%o A348623 def A348623gen(): # generator of terms
%o A348623     n = 1
%o A348623     yield n
%o A348623     while True:
%o A348623         n += prod(q+1 for p, q in factorint(n).items() if p > 2)
%o A348623         yield n
%o A348623 A348623_list = list(islice(A348623gen(),20)) # _Chai Wah Wu_, Dec 13 2021
%Y A348623 Cf. A001227, A064491.
%K A348623 nonn
%O A348623 1,2
%A A348623 _Patryk Kisieniowski_, Oct 25 2021