A362402 Positive numbers m such that a record number of numbers k have m as the sum of divisors of k that have a square factor (A162296).
1, 4, 48, 72, 216, 288, 864, 1440, 1728, 2880, 3456, 4320, 5184, 5760, 8640, 12096, 17280, 25920, 34560, 48384, 51840, 69120, 103680, 120960, 155520, 181440, 207360, 241920, 311040, 362880, 483840, 622080, 725760, 967680, 1088640, 1209600, 1451520, 2177280, 2903040
Offset: 1
Keywords
Links
- Amiram Eldar, Table of n, a(n) for n = 1..60
Programs
-
Mathematica
s[n_] := Module[{f = FactorInteger[n], p, e}, p = f[[;; , 1]]; e = f[[;; , 2]]; Times @@ ((p^(e + 1) - 1)/(p - 1)) - Times @@ (p + 1)]; s[1] = 0; seq[max_] := Module[{v = Select[Array[s, max], 0 < # <= max &], sq = {1}, t, tmax = 0}, t = Sort[Tally[v]]; Do[If[t[[k]][[2]] > tmax, tmax = t[[k]][[2]]; AppendTo[sq, t[[k]][[1]]]], {k, 1, Length[t]}]; sq]; seq[10^5] -
PARI
s(n) = {my(f = factor(n), p, e); prod(i = 1, #f~, p = f[i, 1]; e = f[i, 2]; ((p^(e + 1) - 1)/(p - 1))) - prod(i = 1, #f~, f[i, 1] + 1);} lista(kmax) = {my(v = vector(kmax), vmax = 0, i); for(k=1, kmax, i = s(k); if(i > 0 && i <= kmax, v[i]++)); print1(1, ", "); for(k=1, kmax, if(v[k] > vmax, vmax = v[k]; print1(k, ", "))); }
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