A381844 - OEIS

%I #40 Sep 22 2025 16:01:36

%S 1,3,5,7,11,19,23,34,91,105,209,221,231,385,399,429,481,609,665,715,

%T 805,897,1001,1105,1430,1729,1870,2046,2233,2261,3094,3230,3553,3565,

%U 3774,4278,4862,4921,4945,5270,5358,5365,6409,6670,7429,7462,7657,7990,8041,8569

%N Quotients of A380487.

%C Sequence is strictly increasing based on definition of A380487.

%H Robert Israel, <a href="/A381844/b381844.txt">Table of n, a(n) for n = 1..168</a>

%e 1 is a term because rad(2)/sopf(2) = 2/2.

%e 3 is a term because rad(30)/sopf(30) = 30/10.

%e 5 is a term because rad(70)/sopf(70) = 70/14.

%p f:= proc(n,m) local q,S;

%p    S:= numtheory:-factorset(n);

%p    q:= convert(S,`*`)/convert(S,`+`);

%p    if q::integer and q > m  then q else 0 fi;

%p end proc:

%p m:= 0: R:= NULL: count:= 0:

%p for n from 2 while count < 50 do

%p   v:= f(n,m);

%p   if v > 0 then

%p     m:= v; R:= R,v; count:= count+1;

%p   fi;

%p od:

%p R; # _Robert Israel_, Apr 30 2025

%o (SageMath)

%o def sopf(n): return sum(set(prime_factors(n)))

%o def rad(n):

%o     rad = 1

%o     for p in set(prime_factors(n)): rad *= p

%o     return rad

%o def output(limit=39):

%o     results = []

%o     n = 2

%o     result = 0

%o     while len(results) < limit:

%o         sopf_n = sopf(n)

%o         rad_n = rad(n)

%o         if rad_n % sopf_n == 0 and result < rad_n / sopf_n:

%o             result = rad_n / sopf_n

%o             print(result, end=', ')

%o         n += 1

%o     return

%o output()

%o (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 Cf. A007947, A008472, A380487.

%K nonn

%O 1,2

%A _Torlach Rush_, Mar 10 2025