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A381844 Quotients of A380487.

%I A381844 #39 May 02 2025 04:22:20
%S A381844 1,3,5,7,11,19,23,34,91,105,209,221,231,385,399,429,481,609,665,715,
%T A381844 805,897,1001,1105,1430,1729,1870,2046,2233,2261,3094,3230,3553,3565,
%U A381844 3774,4278,4862,4921,4945,5270,5358,5365,6409,6670,7429,7462,7657,7990,8041,8569
%N A381844 Quotients of A380487.
%C A381844 Sequence is strictly increasing based on definition of A380487.
%H A381844 Robert Israel, <a href="/A381844/b381844.txt">Table of n, a(n) for n = 1..168</a>
%e A381844 1 is a term because rad(2)/sopf(2) = 2/2.
%e A381844 3 is a term because rad(30)/sopf(30) = 30/10.
%e A381844 5 is a term because rad(70)/sopf(70) = 70/14.
%p A381844 f:= proc(n,m) local q,S;
%p A381844    S:= numtheory:-factorset(n);
%p A381844    q:= convert(S,`*`)/convert(S,`+`);
%p A381844    if q::integer and q > m  then q else 0 fi;
%p A381844 end proc:
%p A381844 m:= 0: R:= NULL: count:= 0:
%p A381844 for n from 2 while count < 50 do
%p A381844   v:= f(n,m);
%p A381844   if v > 0 then
%p A381844     m:= v; R:= R,v; count:= count+1;
%p A381844   fi;
%p A381844 od:
%p A381844 R; # _Robert Israel_, Apr 30 2025
%o A381844 (Sage)
%o A381844 def sopf(n): return sum(set(prime_factors(n)))
%o A381844 def rad(n):
%o A381844     rad = 1
%o A381844     for p in set(prime_factors(n)): rad *= p
%o A381844     return rad
%o A381844 def output(limit=39):
%o A381844     results = []
%o A381844     n = 2
%o A381844     result = 0
%o A381844     while len(results) < limit:
%o A381844         sopf_n = sopf(n)
%o A381844         rad_n = rad(n)
%o A381844         if rad_n % sopf_n == 0 and result < rad_n / sopf_n:
%o A381844             result = rad_n / sopf_n
%o A381844             print(result, end=', ')
%o A381844         n += 1
%o A381844     return
%o A381844 output()
%o A381844 (PARI) lista(nn) = my(m=0, list=List()); for (n=2, nn, my(f=factor(n)[,1], q=factorback(f)/vecsum(f)); if ((denominator(q) == 1) && (q>m), listput(list, q); m=q);); Vec(list); \\ _Michel Marcus_, Mar 29 2025
%Y A381844 Cf. A007947, A008472, A380487.
%K A381844 nonn
%O A381844 1,2
%A A381844 _Torlach Rush_, Mar 10 2025