OFFSET
2,2
COMMENTS
For n>= 11, terms were computed with 2nd PARI program using the T. D. Noe algorithm.
LINKS
Michael De Vlieger, Table of n, a(n) for n = 2..27
EXAMPLE
From Michael De Vlieger, May 22 2025: (Start)
Table of a(n), n = 2..10, showing prime power decomposition:
Prime power
factor exponent
111
n m = a(n) sigma(m) n*m/2 2357137
------------------------------------------------
2 1 1 1 0
3 2 3 3 1
4 6 12 12 11
5 24 60 60 31
6 120 360 360 311
7 1680 5952 5880 4111
8 27720 112320 110880 32111
9 720720 3249792 3243240 421111
10 122522400 614210688 612612000 5221111 (End)
MATHEMATICA
(* First, load function f from A025487, then *)
nn = 12; s = Union@ Flatten@ f[nn + 4]; m = Length[s];
Monitor[Reap[Do[k = 1; While[And[DivisorSigma[1, #] < n*#/2 &[ s[[k]] ], k < m], k++]; If[k == m, Break[], Sow[s[[k]] ] ], {n, 2, nn}] ][[-1, 1]], n] (* Michael De Vlieger, May 21 2025 *)
PROG
(PARI) a(n) = my(k=1); while (sigma(k) < k*n/2, k++); k;
(PARI) ab(x) = sigma(x)/x;
findpos(vca, val) = for (i=1, #vca -1, if ((sigma(vca[i])/vca[i] < val) && (sigma(vca[i+1])/vca[i+1] > val), return(i)); );
a(n) = if (n==1, return(0)); if (n==2, return(1)); my(val = n/2, vca = readvec("c:/gp/bfiles/b004490.txt"), vsa = readvec("c:/gp/bfiles/b004394.txt"), wc = select(x->(ab(x) == val), vca)); if (#wc, return(wc[1])); my(ipos = findpos(vca, val), c1 = vca[ipos], c2 = vca[ipos+1], ws = select(x->((x>c1) && (x<=c2)), vsa)); for (i=1, #ws, if (ab(ws[i]) >= val, return(ws[i])); );
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Marcus, May 15 2025
STATUS
approved