This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A339939 #11 Aug 17 2025 13:08:10
%S A339939 4900,14700,53900,63700,83300,93100,112700,142100,151900,161700,
%T A339939 181300,191100,200900,210700,230300,249900,259700,279300,289100,
%U A339939 298900,328300,338100,347900,349448,357700,387100,406700,426300,436100,455700,475300,494900,504700,524300
%N A339939 Coreful weird numbers: numbers k that are coreful abundant (A308053) but no subset of their aliquot coreful divisors sums to k.
%C A339939 First differs from A321146 at n = 24.
%C A339939 A coreful divisor d of a number k is a divisor with the same set of distinct prime factors as k, or rad(d) = rad(k), where rad(k) is the largest squarefree divisor of k (A007947).
%H A339939 Amiram Eldar, <a href="/A339939/b339939.txt">Table of n, a(n) for n = 1..1000</a>
%e A339939 4900 is a term since the sum of its aliquot coreful divisors, {70, 140, 350, 490, 700, 980, 2450}, is 5180 > 4900, and no subset of these divisors sums to 4900.
%t A339939 corDiv[n_] := Module[{rad = Times @@ FactorInteger [n][[;;,1]]}, rad * Divisors[n/rad]]; corWeirdQ[n_] := Module[{d = Most@corDiv[n], x}, Plus @@ d > n && SeriesCoefficient[Series[Product[1 + x^d[[i]], {i, Length[d]}], {x, 0, n}], n] == 0]; Select[Range[10^5], corWeirdQ]
%Y A339939 Subsequence of A308053.
%Y A339939 Cf. A007947, A057723.
%Y A339939 Similar sequences: A006037, A064114, A292986, A306984, A321146, A327948.
%K A339939 nonn
%O A339939 1,1
%A A339939 _Amiram Eldar_, Dec 23 2020