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 A173431 #8 Jul 22 2025 07:50:38 %S A173431 1,6,5,4,2,1,3,2,3,1,2,1,2,1,1,5,2,1,2,1,4,1,2,1,5,1,2,1,2,1,4,3,1,1, %T A173431 2,2,2,1,2,1,2,1,2,1,1,1,2,1,3,4,1,1,2,1,2,1,2,1,2,1,2,1,2,4,2,1,2,1, %U A173431 1,1,2,1,2,1,2,1,2,1,2,1,4,1,2,1,2,1,1,1,2,1,1,1,3,1,1,1,4,3,1,5,2,1,2,1,1 %N A173431 Count of consecutive coprime iterations of sum-of-divisors function. %C A173431 The last of these iterates is the value in A173430. %D A173431 Graeme L. Cohen and Herman J. J. te Riele, Iterating the sum-of-divisors function, Experimental Mathematics, 5 (1996), pp. 93-100. %D A173431 Oystein Ore, Number Theory and Its History, 1988, Dover Publications, ISBN 0486656209, pp. 88-96. %H A173431 Leonard Eugene Dickson, History of the Theory of Numbers, <a href="http://books.google.com/books?id=mbk9AAAAYAAJ">Volume I</a>, Divisibility and Primality, Carnegie Institution of Washington, 1919, Chapters II and X %e A173431 Calculating sum-of-divisors ( ... sum-of-divisors ( sum-of-divisors ( 7 ) ) ... ) the iterates are 7, 8, 15, 24, ... . %e A173431 The initial, consecutive, pairwise, coprime iterates are 7, 8, 15, and there are 3 of these, so a(7) = 3. %e A173431 Here sigma ( 7 ) = 8, sigma ( sigma ( 7 ) ) = sigma ( 8 ) = 15, etc. %o A173431 (PARI) a(n)=my(t,s);if(n==1,1,while(1,s++;t=sigma(n);if(gcd(t,n)==1,n=t,return(s)))) \\ _Charles R Greathouse IV_, Feb 06 2012 %Y A173431 Cf. A173430, A129246 and the references there, A019294, A019295, A000203, A051027, A019284, A019277. %K A173431 easy,nonn %O A173431 1,2 %A A173431 _Walter Nissen_, Feb 18 2010