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%I #7 Aug 09 2020 00:33:23
%S 0,0,0,0,0,1,0,0,0,0,0,2,0,0,0,0,0,1,0,1,0,0,0,3,0,0,0,1,0,1,0,0,0,0,
%T 0,2,0,0,0,2,0,1,0,0,0,0,0,4,0,0,0,0,0,1,0,2,0,0,0,2,0,0,0,0,0,1,0,0,
%U 0,1,0,3,0,0,0,0,0,1,0,3,0,0,0,2,0,0,0,1,0,1,0,0,0,0,0,5,0,0,0,1,0,1,0,1,0
%N Number of iterations of x -> A252463(x) needed before the result is deficient, when starting from x=n.
%H Antti Karttunen, <a href="/A336917/b336917.txt">Table of n, a(n) for n = 1..65537</a>
%F For all n >= 0, a(A007283(n)) = n.
%e For n = 945, the first odd abundant number, the iteration of A252463 proceeds as 945 -> 120 -> 60 -> 30 -> 15 -> 6 -> 3 -> 2 -> 1. From 945 to 30, all are nondeficient (sigma(k) >= 2k), and only at 15 we encounter the first deficient number, as sigma(15) = 24 < 2*15. Therefore a(945) = 4.
%o (PARI)
%o A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
%o A252463(n) = if(!(n%2),n/2,A064989(n));
%o A336917(n) = { my(i=0); while(sigma(n) >= (2*n), n = A252463(n); i++); (i); };
%Y Cf. A005100, A007283, A023196, A064989, A252463, A294934, A336389, A336834, A336835, A336915.
%K nonn
%O 1,12
%A _Antti Karttunen_, Aug 08 2020
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