cp's OEIS Frontend

A261088 Number of steps needed to reach zero when starting from k = n^2 and repeatedly applying the map that replaces k with k - d(k), where d(k) is the number of divisors of k (A000005).

%I A261088 #12 Mar 30 2017 21:58:46
%S A261088 0,1,2,3,5,6,10,10,19,15,19,21,24,28,39,33,53,44,49,53,60,61,69,72,79,
%T A261088 82,92,93,117,108,115,115,140,121,174,146,205,155,233,217,267,192,295,
%U A261088 209,225,222,238,249,267,270,299,290,336,313,373,328,411,347,451,380,486,400,534,422,447,441,460,460,511,479,496,504,545,529,602,553,579,577,626,612,681,632,747,665,796,695
%N A261088 Number of steps needed to reach zero when starting from k = n^2 and repeatedly applying the map that replaces k with k - d(k), where d(k) is the number of divisors of k (A000005).
%H A261088 Antti Karttunen, <a href="/A261088/b261088.txt">Table of n, a(n) for n = 0..5792</a>
%F A261088 a(n) = A155043(A000290(n)) = A155043(n^2).
%t A261088 f[n_]:=Length[NestWhileList[#-DivisorSigma[0,#]&,n^2,#!= 0&]]-1;f/@Range[0,85] (* _Ivan N. Ianakiev_, Sep 25 2015 *)
%o A261088 (PARI)
%o A261088 allocatemem((2^31)+(2^30));
%o A261088 uplim = 2^25;
%o A261088 v155043 = vector(uplim);
%o A261088 v155043[1] = 1; v155043[2] = 1;
%o A261088 for(i=3, uplim, v155043[i] = 1 + v155043[i-numdiv(i)]; if(!(i%65536),print1(i,", ")););
%o A261088 A155043 = n -> if(!n,n,v155043[n]);
%o A261088 A261088 = n -> A155043(n^2);
%o A261088 for(n=0, 5792, write("b261088.txt", n, " ", A261088(n)));
%o A261088 (Scheme) (define (A261088 n) (A155043 (A000290 n)))
%Y A261088 Cf. A000005, A000290, A155043, A049820, A259934, A261085.
%Y A261088 Cf. also A260732, A261222.
%K A261088 nonn
%O A261088 0,3
%A A261088 _Antti Karttunen_, Sep 23 2015