A288070 a(n) is the least number that enters a cycle of length 2n in the iteration sequence s(0)=n, s(k+1) = s(k) + (-1)^k*d(s(k)), where d(n) is the number of divisors of n (A000005).

3, 93, 273, 1617, 684, 3993, 58695, 91355, 572793, 167055, 441519, 13991016, 2337513, 20225991, 48163788, 20625997, 148789675, 470944675, 626064036, 506112555, 963071088, 494359089, 3252701700, 3972446520, 4515893681, 3472027000, 9096968436

Offset

1,1

Links

Table of n, a(n) for n=1..27.

Claudia Spiro, An Iteration Problem Involving the Divisor Function, Acta Arithmetica, Vol. 46, No. 3 (1986), pp. 215-225.

Mathematica

nmax=10; lst=ConstantArray[0, nmax]; For[n=2, n<10^6, n++; c=1; v={}; m=0; s=1; a=n; i={}; While[m<10^6, AppendTo[v, a]; If[Length[v] > 3, i=LongestCommonSubsequencePositions[v[[1;; -3]], v[[-2;; -1]]], i = {}];
If[Length[i]==2 && Differences[i[[1]]][[1]]==1, c=Length[v]-i[[1]][[1]]-1; Break[]]; m++; a = a + s*DivisorSigma[0, a]; s = -s; ]; If[c/2<nmax && lst[[c/2]] == 0, lst[[c/2]]=n]]; lst (* Amiram Eldar, Jun 05 2017 *)

Prog

(PARI) findpos(v, new) = {for(i=1, #v, if (v[#v-i+1] == new, return (i)); ); }
loop(n) = {my(k = 1, ok = 0, v = []); while(!ok, new = n + k*numdiv(n); if (pos = findpos (v, new), if (#v > pos, if (v[#v] == v[#v - pos], return (pos)); ); ); n = new; k = -k; v = concat(v, new); ); }
a(n) = my(k=3); while (loop(k) != 2*n, k++); k;

Crossrefs

Cf. A000005, A049820, A062249, A175304 (numbers with cycle of length 2), A285004 (records of this sequence).

Sequence in context: A297479 A116161 A285004 * A116292 A139543 A241982

Adjacent sequences: A288067 A288068 A288069 * A288071 A288072 A288073

Keyword

nonn,more

Author

Michel Marcus, Jun 05 2017

Extensions

a(19)-a(27) from Giovanni Resta, Jun 06 2017

Status

approved