A368063 a(n) is the least number k such that sigma(sigma(k) * k) > n * sigma(k) * k.

1, 2, 3, 10, 160, 12155, 26558675

Offset: 0

Author

Max Z. Scialabba, Dec 10 2023

Keywords

• nonn
• more

Comments

Application of A134716 (sigma(k) / k > n) to A064987.

From Daniel Suteu, Dec 21 2023: (Start)

a(7) <= 114775357632650.

a(8) <= 272113056574982766111055794421. (End)

Examples

			For n = 4, the divisors of 160 sum to 378. 160 * 378 = 60480, whose divisors sum up to 243840 > 4 * 60480.
		

Crossrefs

Cf. A064987, A134716.

Programs

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;
    }

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 *)

PARI

a(n) = my(k=1); while (sigma(sigma(k)*k) <= n * sigma(k) * k, k++); k; \\ Michel Marcus, Dec 10 2023

Extensions

a(6) from Michel Marcus, Dec 10 2023