|
|
A324711
|
|
Number x such that sigma(x) = Sum_{i=1..k} {sigma(x/p_i)}, where p_i are the k prime factors of x.
|
|
3
|
|
|
8580, 16632, 24840, 35910, 38280, 53130, 161040, 186732, 276276, 429780, 598290, 833112, 1232616, 1297890, 1631448, 2661330, 2781000, 2875740, 3111108, 3233790, 3449640, 3504816, 3754920, 4901160, 5185488, 5211570, 5948250, 6749028, 8066640, 9006984, 10750080
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
LINKS
|
|
|
EXAMPLE
|
Prime factors of 8580 are 2, 3, 5, 11, 13 and sigma(8580) = 28224, sigma(8580/2) + sigma(8580/3) + sigma(8580/5) + sigma(8580/11) + sigma(8580/13) = 12096 + 7056 + 4704 + 2352 + 2016 = 28224.
|
|
MAPLE
|
with(numtheory): P:=proc(q) local k, n; for n from 1 to q do
if sigma(n)=add(sigma(n/k), k=factorset(n)) then print(n);
fi; od; end: P(10^9);
|
|
MATHEMATICA
|
Select[Range[2, 60000], DivisorSigma[1, #] == Total@DivisorSigma[1, #/FactorInteger[#][[;; , 1]]] &] (* Amiram Eldar, Mar 20 2019 *)
|
|
PROG
|
(PARI) isok(x) = my(f=factor(x)[, 1]~); sigma(x) == sum(k=1, #f, sigma(x/f[k])); \\ Michel Marcus, Mar 15 2019
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|