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).

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, 82, 92, 93, 117, 108, 115, 115, 140, 121, 174, 146, 205, 155, 233, 217, 267, 192, 295, 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

Offset

0,3

Links

Antti Karttunen, Table of n, a(n) for n = 0..5792

Formula

a(n) = A155043(A000290(n)) = A155043(n^2).

Mathematica

f[n_]:=Length[NestWhileList[#-DivisorSigma[0, #]&, n^2, #!= 0&]]-1; f/@Range[0, 85] (* Ivan N. Ianakiev, Sep 25 2015 *)

Prog

(PARI)
allocatemem((2^31)+(2^30));
uplim = 2^25;
v155043 = vector(uplim);
v155043[1] = 1; v155043[2] = 1;
for(i=3, uplim, v155043[i] = 1 + v155043[i-numdiv(i)]; if(!(i%65536), print1(i, ", ")); );
A155043 = n -> if(!n, n, v155043[n]);
A261088 = n -> A155043(n^2);
for(n=0, 5792, write("b261088.txt", n, " ", A261088(n)));
(Scheme) (define (A261088 n) (A155043 (A000290 n)))

Crossrefs

Cf. A000005, A000290, A155043, A049820, A259934, A261085.

Cf. also A260732, A261222.

Sequence in context: A133139 A162309 A014593 * A303431 A317709 A034044

Adjacent sequences: A261085 A261086 A261087 * A261089 A261090 A261091

Keyword

nonn

Author

Antti Karttunen, Sep 23 2015

Status

approved