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).

3135, 6279, 8855, 9405, 10695, 11571, 15675, 16095, 17255, 17391, 18837, 20615, 20735, 26691, 28083, 28215, 31031, 32085, 34485, 34713, 36519, 41151, 41615, 43953, 44275, 45695, 46655, 47025, 47859, 48285, 48495, 50439, 52173, 53475, 54131, 56511, 56823, 57239, 59295, 59565

Offset: 1

Author

Paolo Xausa, May 08 2025

Keywords

• nonn

Examples

			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).
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Row n = 4 of A383726.

Cf. A001221, A365795, A382469, A383725, A383726, A383729.

Programs

Maple

N:= 10^5: # for terms <= N
P:= select(isprime,[2,seq(i,i=3..N/(3*5*7),2)]):
V:= NULL:
for j from 1 while P[j]^3*(3*P[j]) < N do
  for k from j+1 while P[j]*P[k]^2*(P[j]+2*P[k]) < N do
    for l from k+1 while P[j]*P[k]*P[l] * (P[j]+P[k]+P[l]) <= N do
      p4:= P[j]+P[k]+P[l];
      if not isprime(p4) then next fi;
      for d1 from 1 while P[j]^d1 * P[k] * P[l] * p4 <= N do
       for d2 from 1 while P[j]^d1 * P[k]^d2 * P[l] * p4 <= N do
        for d3 from 1 while P[j]^d1 * P[k]^d2 * P[l]^d3  * p4 <= N do
         for d4 from 1 while  P[j]^d1 * P[k]^d2 * P[l]^d3 * p4^d4 <= N do
             V:= V,P[j]^d1 * P[k]^d2 * P[l]^d3 * p4^d4
od od od od od od od:
sort([V]); # Robert Israel, Jun 09 2025

Mathematica

A383728Q[k_] := Length[#] == 4 && Total[Most[#]] == Last[#] & [FactorInteger[k][[All, 1]]];
Select[Range[10^5], A383728Q]