A064440 Numbers k such that A048138(k) is a prime and sets a new record for such primes.

6, 21, 31, 79, 121, 265, 271, 379, 541, 631, 1051, 1351, 1597, 1711, 2071, 2401, 2551, 2761, 2881, 2941, 3811, 4111, 4471, 4531, 4621, 5251, 6091, 8341, 8371, 8401, 8821, 9871, 11551, 13651, 16171, 19531, 21211, 22681, 23101, 27931, 30661, 32551, 33811, 37591

Offset: 1

Author

Jason Earls, Oct 01 2001

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..188

Crossrefs

Cf. A001065, A048138, A238895, A238896.

Programs

Mathematica

seq[max_] := Module[{s = Table[0, {n, 1, max}], i, v = {}, m = 0}, Do[If[(i = DivisorSigma[1, n] - n) <= max, s[[i]]++], {n, 2, (max - 1)^2}]; Do[If[s[[i]] > m && PrimeQ[s[[i]]], m = s[[i]]; AppendTo[v, i]], {i, 1, max}]; v]; seq[2000] (* Amiram Eldar, Sep 23 2022 *)

PARI

f(n) = my(s=0); for(x=1,n^2, if(sigma(x)-x==n,s++)); s;
a=0; for(n=1,10^5,x=f(n); if(isprime(x),b=x; if(b>a,a=b; print1(n, ", "))))

Extensions

Corrected and extended by Matthew Conroy, Oct 02 2001

a(11)-a(44) from Amiram Eldar, Oct 01 2019