OFFSET
0,1
COMMENTS
In the first 1000 terms the most repeated number is 719 with 14 occurrences.
What can we say about records in this sequence? - David A. Corneth, May 10 2017
LINKS
David A. Corneth, Table of n, a(n) for n = 0..9999
EXAMPLE
a(3) = 369: sigma(369) = sigma(180) = 369 + 180 - 3 = 546;
a(4) = 26: sigma(26) = sigma(20) = 26 + 20 - 4 = 42;
a(5) = 11: sigma(11) = sigma(6) = 11 + 6 - 5 = 12.
From David A. Corneth, May 10 2017 (Start):
a(35) = 69: sigma(62) = sigma(69) = 62 + 69 - 35 = 96.
After creating a list of pairs (sigma(i), i) and sorting them with respect to sigma(i), we get {[1, 1], [3, 2], [4, 3], [6, 5], [7, 4], [8, 7], [12, 6], [12, 11], [13, 9], ...}. Skimming through this list we see that the first pair of numbers having the same value for sigma are 6 and 11. As sigma(y) = x + y - n, we have n = x + y - sigma(y), giving n = 6 + 11 - 12 = 5. We have found no value for a(5) yet, therefore, a(5) = 11. (End)
MAPLE
with(numtheory): P:=proc(q) local a, b, k, n; for n from 0 to q do for k from 1 to q do
a:=sigma(k)-k+n; b:=sigma(a)-a+n; if a>0 and b=k and a<>b then print(a); break;
fi; od; od; end: P(10^9);
MATHEMATICA
Do[m = 1; While[Set[k, Module[{k = n + Boole[n == 0]}, While[! Xor[DivisorSigma[1, m] == DivisorSigma[1, k] == m + k - n, k >= m], k++]; k]] >= m, m++]; Print@ m, {n, 0, 50}] (* Michael De Vlieger, Apr 28 2017 (note: due to size of a(1) program takes a few minutes to run but posts results as soon as they are calculated.) *)
PROG
(PARI) upto(n, {u=50000}) = {my(res = vector(n, i, -1), v=vecsort(vector(u, i, [sigma(i), i])), t=1, u=2); while(u<=#v, if(v[t][1]==v[u][1], i=v[t][2] + v[u][2] - v[t][1]; if(1<=i && i<=n && res[i] == -1, res[i] = v[u][2]); u++, t++; u=t+1)); concat(284, res)} \\ (u is an estimate of the maximum of terms a(n) up to n) David A. Corneth, May 10 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paolo P. Lava, Apr 28 2017
EXTENSIONS
a(35) corrected by David A. Corneth, May 10 2017
STATUS
approved