A381844 Quotients of A380487.

1, 3, 5, 7, 11, 19, 23, 34, 91, 105, 209, 221, 231, 385, 399, 429, 481, 609, 665, 715, 805, 897, 1001, 1105, 1430, 1729, 1870, 2046, 2233, 2261, 3094, 3230, 3553, 3565, 3774, 4278, 4862, 4921, 4945, 5270, 5358, 5365, 6409, 6670, 7429, 7462, 7657, 7990, 8041, 8569

Offset

1,2

Comments

Sequence is strictly increasing based on definition of A380487.

Links

Robert Israel, Table of n, a(n) for n = 1..168

Example

1 is a term because rad(2)/sopf(2) = 2/2.
3 is a term because rad(30)/sopf(30) = 30/10.
5 is a term because rad(70)/sopf(70) = 70/14.

Maple

f:= proc(n, m) local q, S;
   S:= numtheory:-factorset(n);
   q:= convert(S, `*`)/convert(S, `+`);
   if q::integer and q > m  then q else 0 fi;
end proc:
m:= 0: R:= NULL: count:= 0:
for n from 2 while count < 50 do
  v:= f(n, m);
  if v > 0 then
    m:= v; R:= R, v; count:= count+1;
  fi;
od:
R; # Robert Israel, Apr 30 2025

Prog

(SageMath)
def sopf(n): return sum(set(prime_factors(n)))
def rad(n):
    rad = 1
    for p in set(prime_factors(n)): rad *= p
    return rad
def output(limit=39):
    results = []
    n = 2
    result = 0
    while len(results) < limit:
        sopf_n = sopf(n)
        rad_n = rad(n)
        if rad_n % sopf_n == 0 and result < rad_n / sopf_n:
            result = rad_n / sopf_n
            print(result, end=', ')
        n += 1
    return
output()
(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

Crossrefs

Cf. A007947, A008472, A380487.

Sequence in context: A246533 A111052 A138536 * A093929 A144427 A082603

Adjacent sequences: A381841 A381842 A381843 * A381845 A381846 A381847

Keyword

nonn

Author

Torlach Rush, Mar 10 2025

Status

approved