A362403 Number of times that the number A362402(n) occurs as a sum of divisors that have a square factor (A162296).

0, 1, 2, 3, 5, 7, 9, 10, 13, 15, 16, 20, 22, 23, 28, 34, 46, 53, 60, 62, 78, 81, 113, 115, 122, 132, 154, 184, 185, 222, 248, 254, 343, 346, 350, 354, 497, 569, 701, 711, 860, 941, 1088, 1221, 1222, 1235, 1263, 1306, 1572, 1721, 1737, 1948, 2191, 2315, 2418, 2877

Offset: 1

Author

Amiram Eldar, Apr 18 2023

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..60

Crossrefs

Cf. A162296, A362401, A362402.

Similar sequences: A131934, A101373, A206027, A238896.

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 = {0}, t, tmax = 0}, t = Sort[Tally[v]]; Do[If[t[[k]][[2]] > tmax, tmax = t[[k]][[2]]; AppendTo[sq, t[[k]][[2]]]], {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(0, ", "); for(k=1, kmax, if(v[k] > vmax, vmax = v[k]; print1(v[k], ", "))); }