A325307 a(n) = k / (sum of prime factors of k, counted with multiplicity) where k is the n-th number for which the ratio is an integer.

1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 3, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 5, 1, 6, 1, 1, 1, 6, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 10, 1, 1, 1, 1, 1, 1, 12, 1, 1, 1, 1, 1, 1, 11, 1, 1, 1, 11, 1, 1, 15, 1, 1, 16, 1, 1, 1, 1, 1, 1, 1, 11, 18, 1, 1, 14, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 21, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 20, 1, 1, 25

Offset

1,8

Links

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

Example

a(8) = 2 comes from k = A036844(8) = 16 = 2^4. The sum of prime factors is 2 + 2 + 2 + 2 = 8, so k/(sum of prime factors of k) = 2.

Maple

Res:= NULL: count:= 0:
for n from 2 while count < 200 do
  F:= ifactors(n)[2];
  r:= n /add(t[1]*t[2], t=F);
  if r::integer then count:= count+1; Res:= Res, r fi
od:
Res; # Robert Israel, Jul 29 2019

Mathematica

Select[Array[#/Total@ Flatten[ConstantArray[#1, #2] & @@ # & /@ FactorInteger[#]] &, 450, 2], IntegerQ] (* Michael De Vlieger, Apr 21 2019 *)

Prog

(Python)
maxNum = 455
ratios = []
for i in range(2, maxNum):
  sumFactors = A001414(i)
  if i % sumFactors == 0:
    ratio = i // sumFactors
    ratios.append(ratio)
print(ratios) # ratios is an array that contains the sequence

Crossrefs

Cf. A001414 (sum of prime factors), A036844 (values of k).

Sequence in context: A105540 A356958 A057043 * A211095 A070091 A091981

Adjacent sequences: A325304 A325305 A325306 * A325308 A325309 A325310

Keyword

nonn

Author

Sven Kunze, Apr 20 2019

Status

approved