|
|
A173582
|
|
Numbers k such that sigma(tau(k)) = rad(k).
|
|
1
|
|
|
1, 3, 135, 336, 343, 375, 1134, 14406, 24336, 41067, 54756, 85293, 321408, 428544, 430080, 1028196, 1084752, 1651104, 1886976, 2476656, 2935296, 3066336, 3341637, 3577392, 4599504, 4881384, 5133375, 5366088, 5451264, 8347248, 8989344, 9240075, 9552816, 9871875
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
rad(k) is the product of the primes dividing k (A007947), tau(k) is the number of divisors of k (A000005), sigma(k) is the sum of divisor of k (A000203).
|
|
LINKS
|
|
|
FORMULA
|
|
|
EXAMPLE
|
tau(3) = 2, sigma(2) = 3 and rad(3) = 3. tau(135) = 8, sigma(8) = 15 and rad(135) = 15. tau(14406) = 20, sigma(20) = 42 and rad(14406) = 42.
|
|
MAPLE
|
with(numtheory):for n from 1 to 1000000 do : t1:= ifactors(n)[2] : t2 :=sum(t1[i][1], i=1..nops(t1)):if sigma(tau(n)) = t2 then print (n): else fi : od :
|
|
MATHEMATICA
|
Select[Range[500000], DivisorSigma[1, DivisorSigma[0, #]] == Times @@ (First@# & /@ FactorInteger[#]) &] (* Amiram Eldar, Jul 11 2019 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|