login
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.
2
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
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
KEYWORD
nonn
AUTHOR
Sven Kunze, Apr 20 2019
STATUS
approved