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 A378859 #17 Jan 29 2025 22:13:14
%S A378859 72,108,200,288,392,432,500,648,800,864,968,972,1152,1352,1372,1568,
%T A378859 1800,1944,2000,2592,2700,3200,3456,3528,3872,3888,4000,4500,4608,
%U A378859 5000,5292,5400,5408,5488,6272,6912,7200,8712,8748,9000,9248,9800,10368,10584,10800,10976,11552,12168,12348,12500,12800,13068,13500,14112,15488
%N A378859 Achilles numbers that are abundant.
%C A378859 33075 is the smallest odd term.
%C A378859 The set of distinct prime factors of a term can be any set P of primes such that Product_{p in P} p/(p-1) > 2. - _Robert Israel_, Jan 29 2025
%H A378859 Robert Israel, <a href="/A378859/b378859.txt">Table of n, a(n) for n = 1..10000</a>
%e A378859 72=2^3*3^2 is a term because it is an Achilles number (powerful but imperfect, see A052486) and it is smaller than the sum of its proper divisors (1+2+3+4+6+8+9+12+18+24+36=123).
%e A378859 108=2^2*3^3 is a term because it is an Achilles number (powerful but imperfect, see A052486) and it is smaller than the sum of its proper divisors (1+2+3+4+6+9+12+18+27+36+54=172).
%p A378859 filter:= proc(n) local F, E, t; F:= ifactors(n)[2]; E:= F[..,2]; min(E)>1 and igcd(op(E))=1 and mul((t[1]^(1+t[2])-1)/(t[1]-1), t = F) > 2*n end proc:
%p A378859 select(filter, [$1..10^5]); # _Robert Israel_, Jan 28 2025
%t A378859 q[n_] := Module[{f = FactorInteger[n], p, e}, p = f[[;; , 1]]; e = f[[;; , 2]]; AllTrue[e, # > 1 &] && GCD @@ e == 1 && Times @@ ((p - 1/p^e)/(p - 1)) > 2]; Select[Range[16000], q] (* _Amiram Eldar_, Dec 09 2024 *)
%Y A378859 Intersection of A005101 and A052486.
%K A378859 nonn
%O A378859 1,1
%A A378859 _Massimo Kofler_, Dec 09 2024