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
Links
- Claudia Spiro, An Iteration Problem Involving the Divisor Function, Acta Arithmetica, Vol. 46, No. 3 (1986), pp. 215-225.
Crossrefs
Programs
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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/2Amiram Eldar, Jun 05 2017 *) -
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;
Extensions
a(19)-a(27) from Giovanni Resta, Jun 06 2017