cp's OEIS Frontend

A383728 Numbers k such that omega(k) = 4 and the largest prime factor of k equals the sum of its remaining distinct prime factors, where omega(k) = A001221(k).

%I A383728 #11 Jun 09 2025 21:01:25
%S A383728 3135,6279,8855,9405,10695,11571,15675,16095,17255,17391,18837,20615,
%T A383728 20735,26691,28083,28215,31031,32085,34485,34713,36519,41151,41615,
%U A383728 43953,44275,45695,46655,47025,47859,48285,48495,50439,52173,53475,54131,56511,56823,57239,59295,59565
%N A383728 Numbers k such that omega(k) = 4 and the largest prime factor of k equals the sum of its remaining distinct prime factors, where omega(k) = A001221(k).
%H A383728 Robert Israel, <a href="/A383728/b383728.txt">Table of n, a(n) for n = 1..10000</a>
%e A383728 32085 is a term because it has 4 distinct prime factors (3, 5, 23 and 31) and the largest one is the sum of the others (3 + 5 + 23 = 31).
%p A383728 N:= 10^5: # for terms <= N
%p A383728 P:= select(isprime,[2,seq(i,i=3..N/(3*5*7),2)]):
%p A383728 V:= NULL:
%p A383728 for j from 1 while P[j]^3*(3*P[j]) < N do
%p A383728   for k from j+1 while P[j]*P[k]^2*(P[j]+2*P[k]) < N do
%p A383728     for l from k+1 while P[j]*P[k]*P[l] * (P[j]+P[k]+P[l]) <= N do
%p A383728       p4:= P[j]+P[k]+P[l];
%p A383728       if not isprime(p4) then next fi;
%p A383728       for d1 from 1 while P[j]^d1 * P[k] * P[l] * p4 <= N do
%p A383728        for d2 from 1 while P[j]^d1 * P[k]^d2 * P[l] * p4 <= N do
%p A383728         for d3 from 1 while P[j]^d1 * P[k]^d2 * P[l]^d3  * p4 <= N do
%p A383728          for d4 from 1 while  P[j]^d1 * P[k]^d2 * P[l]^d3 * p4^d4 <= N do
%p A383728              V:= V,P[j]^d1 * P[k]^d2 * P[l]^d3 * p4^d4
%p A383728 od od od od od od od:
%p A383728 sort([V]); # _Robert Israel_, Jun 09 2025
%t A383728 A383728Q[k_] := Length[#] == 4 && Total[Most[#]] == Last[#] & [FactorInteger[k][[All, 1]]];
%t A383728 Select[Range[10^5], A383728Q]
%Y A383728 Row n = 4 of A383726.
%Y A383728 Cf. A001221, A365795, A382469, A383725, A383726, A383729.
%K A383728 nonn
%O A383728 1,1
%A A383728 _Paolo Xausa_, May 08 2025