|
|
A368063
|
|
a(n) is the least number k such that sigma(sigma(k) * k) > n * sigma(k) * k.
|
|
0
|
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
a(7) <= 114775357632650.
a(8) <= 272113056574982766111055794421. (End)
|
|
LINKS
|
|
|
EXAMPLE
|
For n = 4, the divisors of 160 sum to 378. 160 * 378 = 60480, whose divisors sum up to 243840 > 4 * 60480.
|
|
MATHEMATICA
|
a={}; For[n=0, n<=6, n++, k=1; While[DivisorSigma[1, DivisorSigma[1, k]k] <= n DivisorSigma[1, k] k, k++]; AppendTo[a, k]]; a (* Stefano Spezia, Dec 10 2023 *)
|
|
PROG
|
(Java)
public static void main(String[] args)
{
long max = 0;
for (long c = 1; c < Math.pow(10, 8); c = c + 1)
{
if (factorSum(factorSum(c) * c) > max * factorSum(c) * c)
{
System.out.println(c + ": " + factorSum(c) * c);
max = max + 1;
}
}
}
public static long factorSum(long n)
{
long sum = 0;
for (long c = 1; c <= Math.sqrt(n); c = c + 1)
{
if (n % c == 0)
{
sum = sum + c;
if (c != Math.sqrt(n))
{
sum = sum + n / c;
}
}
}
return sum;
}
(PARI) a(n) = my(k=1); while (sigma(sigma(k)*k) <= n * sigma(k) * k, k++); k; \\ Michel Marcus, Dec 10 2023
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,more
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|