OFFSET
1,6
COMMENTS
Since the width of the single region of the symmetric representation of sigma( 2^ceiling((p-1)*(log_2 3) - 1) * 3^(p-1) ), for prime number p, at the diagonal equals p, this sequence contains an increasing subsequence (see A250071).
a(n) is also the number of layers of width 1 in the symmetric representation of sigma(n). For more information see A001227. - Omar E. Pol, Dec 13 2016
LINKS
N. J. A. Sloane, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = max_{k=1..floor((sqrt(8*n+1) - 1)/2)} (Sum_{j=1..k}(-1)^(j+1)*A237048(n, j)), for n >= 1.
EXAMPLE
MATHEMATICA
(* function a2[ ] is defined in A249223 *)
a250068[n_]:=Max[a2[n]]
a250068[{m_, n_}]:=Map[a250068, Range[m, n]]
a250068[{1, 100}](* data *)
PROG
(PARI) t237048(n, k) = if (k % 2, (n % k) == 0, ((n - k/2) % k) == 0);
kmax(n) = (sqrt(1+8*n)-1)/2;
t249223(n, k) = sum(j=1, k, (-1)^(j+1)*t237048(n, j));
a(n) = my(wm = t249223(n, 1)); for (k=2, kmax(n), wm = max(wm, t249223(n, k))); wm; \\ Michel Marcus, Sep 20 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
Hartmut F. W. Hoft, Nov 11 2014
STATUS
approved