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A341618 a(n) = 0 if n is not a primitive nondeficient number, otherwise a(n) is the number of primitive nondeficient divisors of the last number in the iteration x -> A003961(x) (starting from x=n) for which that count (A337690) is nonzero.

%I A341618 #12 Feb 24 2021 08:19:05
%S A341618 0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,1,0,0,0,1,0,0,0,1,0,1,0,0,0,0,
%T A341618 0,1,0,0,0,1,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,1,0,0,0,2,0,0,0,0,0,1,0,0,
%U A341618 0,1,0,1,0,0,0,0,0,1,0,1,0,0,0,2,0,0,0,1,0,1,0,0,0,0,0,1,0,0,0,1,0,1,0,1,0,0,0,1,0,0,0,1,0,1,0,0,0,0,0,1
%N A341618 a(n) = 0 if n is not a primitive nondeficient number, otherwise a(n) is the number of primitive nondeficient divisors of the last number in the iteration x -> A003961(x) (starting from x=n) for which that count (A337690) is nonzero.
%H A341618 Antti Karttunen, <a href="/A341618/b341618.txt">Table of n, a(n) for n = 1..65537</a>
%H A341618 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A341618 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%o A341618 (PARI)
%o A341618 A341619(n) = if(sigma(n) < (2*n), 0, fordiv(n, d, if((d<n)&&(sigma(d) >= 2*d), return(0))); (1)); \\ After code in A071395
%o A341618 A337690(n) = sumdiv(n,d,A341619(d));
%o A341618 A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
%o A341618 A341618(n) = { my(t, u=0); while((t=A337690(n))>0, u=t; n = A003961(n)); (u); };
%Y A341618 Differs from A337690 for the first time at n=120, where a(120)=1, while A337690(120)=2.
%Y A341618 Cf. A006039, A341508, A341619, A341624.
%K A341618 nonn
%O A341618 1,60
%A A341618 _Antti Karttunen_, Feb 21 2021