A389299 a(n) is the least number that has exactly n exponential abundant divisors.

1, 900, 3600, 18000, 25200, 108900, 126000, 44100, 88200, 264600, 220500, 396900, 617400, 176400, 485100, 529200, 970200, 882000, 1234800, 1587600, 2425500, 3704400, 4365900, 6174000, 6791400, 5336100, 1940400, 25930800, 6306300, 39690000, 5821200, 92610000, 10672200

Offset

0,2

Comments

36*5^k has k-1 exponential abundant divisors for k >= 1. Therefore, a(n) exists for all n.

Links

Table of n, a(n) for n=0..32.

Mathematica

f[p_, e_] := DivisorSum[e, p^# &]; esigma[1] = 1; esigma[n_] := Times @@ f @@@ FactorInteger[n];
s[n_] := Count[Divisors[n], _?(esigma[#] > 2*# &)];
seq[len_] := Module[{v = Table[0, {len}], c = 0, n = 1, i}, While[c < len, i = s[n] + 1; If[i <= len && v[[i]] == 0, c++; v[[i]] = n]; n++]; v]; seq[14]

Prog

(PARI) esigma(n) = {my(f = factor(n)); prod(k=1, #f~, sumdiv(f[k, 2], d, f[k, 1]^d)); }
s(n) = sumdiv(n, d, esigma(d) > 2*d);
list(len) = {my(v = vector(len), c = 0, n = 1, i); while(c < len, i = s(n) + 1; if(i <= len && v[i] == 0, c++; v[i] = n); n++); v; }

Crossrefs

Cf. A051377, A129575, A389297, A389298, A389300.

Sequence in context: A246887 A232556 A069096 * A232557 A119541 A173486

Adjacent sequences: A389296 A389297 A389298 * A389300 A389301 A389302

Keyword

nonn

Author

Amiram Eldar, Sep 29 2025

Status

approved