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

%I A368063 #44 Dec 22 2023 12:11:45
%S A368063 1,2,3,10,160,12155,26558675
%N A368063 a(n) is the least number k such that sigma(sigma(k) * k) > n * sigma(k) * k.
%C A368063 Application of A134716 (sigma(k) / k > n) to A064987.
%C A368063 From _Daniel Suteu_, Dec 21 2023: (Start)
%C A368063 a(7) <= 114775357632650.
%C A368063 a(8) <= 272113056574982766111055794421. (End)
%e A368063 For n = 4, the divisors of 160 sum to 378. 160 * 378 = 60480, whose divisors sum up to 243840 > 4 * 60480.
%t A368063 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 *)
%o A368063 (Java)
%o A368063 public static void main(String[] args)
%o A368063     {
%o A368063         long max = 0;
%o A368063         for (long c = 1; c < Math.pow(10, 8); c = c + 1)
%o A368063         {
%o A368063             if (factorSum(factorSum(c) * c) > max * factorSum(c) * c)
%o A368063             {
%o A368063                 System.out.println(c + ": " + factorSum(c) * c);
%o A368063                 max = max + 1;
%o A368063             }
%o A368063         }
%o A368063     }
%o A368063     public static long factorSum(long n)
%o A368063     {
%o A368063         long sum = 0;
%o A368063         for (long c = 1; c <= Math.sqrt(n); c = c + 1)
%o A368063         {
%o A368063             if (n % c == 0)
%o A368063             {
%o A368063                 sum = sum + c;
%o A368063                 if (c != Math.sqrt(n))
%o A368063                 {
%o A368063                     sum = sum + n / c;
%o A368063                 }
%o A368063             }
%o A368063         }
%o A368063         return sum;
%o A368063     }
%o A368063 (PARI) a(n) = my(k=1); while (sigma(sigma(k)*k) <= n * sigma(k) * k, k++); k; \\ _Michel Marcus_, Dec 10 2023
%Y A368063 Cf. A064987, A134716.
%K A368063 nonn,more
%O A368063 0,2
%A A368063 _Max Z. Scialabba_, Dec 10 2023
%E A368063 a(6) from _Michel Marcus_, Dec 10 2023