OFFSET
1,2
COMMENTS
If tau(x) + 2*sigma(x) is prime, tau(x) must be odd so x must be a square.
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
EXAMPLE
a(3) = 3 is a term because tau(9) = 3 and sigma(9) = 13 so tau(9) + 2*sigma(9) = 29 and 2*tau(9) + sigma(9) = 19, and 29 and 19 are both prime.
MAPLE
filter:= proc(n) uses numtheory; local s, t;
s:= sigma(n^2); t:= tau(n^2);
isprime(s+2*t) and isprime(2*s+t)
end proc:
select(filter, [$1..10000]);
MATHEMATICA
Select[Range[1800], PrimeQ[(d = DivisorSigma[0, #^2]) + 2*(s = DivisorSigma[1, #^2])] && PrimeQ[2*d + s] &] (* Amiram Eldar, Dec 01 2022 *)
tsQ[n_]:=With[{t=DivisorSigma[0, n^2], s=DivisorSigma[1, n^2]}, AllTrue[{t+2s, 2t+s}, PrimeQ]]; Select[Range[1800], tsQ] (* Harvey P. Dale, Aug 27 2024 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
J. M. Bergot and Robert Israel, Nov 30 2022
STATUS
approved