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A358788 Numbers k such that tau(k^2) + 2*sigma(k^2) and 2*tau(k^2) + sigma(k^2) are both prime. 1
1, 2, 3, 4, 6, 11, 12, 17, 18, 24, 33, 60, 69, 94, 131, 138, 173, 187, 198, 200, 214, 226, 263, 282, 290, 311, 347, 360, 400, 426, 428, 495, 498, 502, 521, 583, 606, 622, 653, 675, 771, 822, 850, 902, 911, 1013, 1020, 1104, 1127, 1177, 1195, 1215, 1243, 1283, 1366, 1377, 1402, 1500, 1714, 1795 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
If tau(x) + 2*sigma(x) is prime, tau(x) must be odd so x must be a square.
LINKS
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 *)
CROSSREFS
Sequence in context: A255921 A111338 A029457 * A014859 A084166 A245569
KEYWORD
nonn
AUTHOR
J. M. Bergot and Robert Israel, Nov 30 2022
STATUS
approved

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Last modified July 21 12:49 EDT 2024. Contains 374474 sequences. (Running on oeis4.)