This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A200815 #25 May 30 2025 03:32:04 %S A200815 0,1,0,2,0,2,1,2,0,3,0,2,2,1,0,3,0,3,2,2,0,3,1,2,2,3,0,3,0,3,2,2,2,2, %T A200815 0,2,2,3,0,3,0,3,3,2,0,3,1,3,2,3,0,3,2,3,2,2,0,4,0,2,3,1,2,3,0,3,2,3, %U A200815 0,4,0,2,3,3,2,3,0,3,1,2,0,4,2,2,2,3,0 %N A200815 Number of iterations of k -> d(k) until n reaches an odd prime. %C A200815 Csajbók and Kasza call this the tau-iteration length. %H A200815 Antti Karttunen, <a href="/A200815/b200815.txt">Table of n, a(n) for n = 3..10000</a> %H A200815 Tímea Csajbók and János Kasza, <a href="https://doi.org/10.71352/ac.35.083">Iterating the tau-function</a>, Annales Univ. Sci. Budapest., Sec. Math. 35 (2011), pp. 83-93. %F A200815 a(n) <= pi(log_2(n)) = A000720(A000523(n)). %F A200815 a(n) = A036459(n)-1 = A060937(n)-2, for n >= 3. - _Antti Karttunen_, Oct 06 2017 %e A200815 d(10) = 4 and d(4) = 3, an odd prime, so a(10) = 2. %t A200815 nop[n_]:=Length[NestWhileList[DivisorSigma[0,#]&,n,#<3 || CompositeQ[ #]&]]-1; Array[ nop,100,3] (* _Harvey P. Dale_, Nov 14 2020 *) %o A200815 (PARI) a(n)=my(i);while(!isprime(n),i++;n=numdiv(n));i %Y A200815 Cf. A036459, A060937, A061286, A200810. %K A200815 nonn %O A200815 3,4 %A A200815 _Charles R Greathouse IV_, Nov 23 2011