OFFSET
1,1
COMMENTS
There are 46 cases below 10^12.
All Mersenne primes are here: sigma((2^((p-1)/2))^2) = sigma(2^(p-1)) = -1 + 2^p, for suitable p.
m is of the form p^(2*e) for some prime p and e > 1 as sigma is multiplicative and m is composite. Terms are sorted by values of m. The sequence isn't monotonic. - David A. Corneth, Jul 18 2020
LINKS
David A. Corneth, Table of n, a(n) for n = 1..10000 (first 100 terms from Harry J. Smith, terms 101-500 from Amiram Eldar)
EXAMPLE
19531 is in the sequence as for the composite m = 125 we have sigma(m^2) = 19531. - David A. Corneth, Jul 18 2020
MATHEMATICA
Do[s=DivisorSigma[1, n]; If[PrimeQ[s]&&!PrimeQ[Sqrt[n]], Print[{n, Sqrt[n], s}]], {n, 1, 20000000}]
PROG
(PARI) { n=0; for (m=1, 10^9, if (isprime(m), next); x=sigma(m^2); if (isprime(x), write("b065403.txt", n++, " ", x); if (n==100, return)) ) } \\ Harry J. Smith, Oct 18 2009
(PARI) upto(n) = {res = List(); forstep(e = 4, logint(n, 2), 2, forprime(p = 2, sqrtnint(n, e), c = (p^(e + 1) - 1)/(p - 1); if(isprime(c), listput(res, [p^e, c]) ) ) ); listsort(res); vector(#res, i, res[i][2]) } \\ David A. Corneth, Jul 18 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Nov 06 2001
EXTENSIONS
Name corrected by David A. Corneth, Jul 18 2020
STATUS
approved