cp's OEIS Frontend

A299153 Numbers k such that sigma(k) and sigma(k^3) are both primes.

%I A299153 #25 Mar 02 2025 14:34:01
%S A299153 4,9,16,25,64,289,2401,7921,3418801,19439281,24730729,40819321,
%T A299153 52258441,67848169,75151561,76405081,142396489,175006441,185313769,
%U A299153 198443569,253541929,352425529,369062521,386554921,414896161,499477801,526105969,684921241,775678201
%N A299153 Numbers k such that sigma(k) and sigma(k^3) are both primes.
%C A299153 Intersection of A023194 and A279096.
%C A299153 All terms are squares.
%H A299153 Chai Wah Wu, <a href="/A299153/b299153.txt">Table of n, a(n) for n = 1..10203</a>
%e A299153 4 is in the sequence because sigma(4) = 7 and sigma(4^2) = 31 are both primes.
%t A299153 Select[Range[10^4], AllTrue[DivisorSigma[1, #] & /@ {#, #^3}, PrimeQ] &] (* _Michael De Vlieger_, Feb 05 2018 *)
%o A299153 (Magma) [n: n in[1..10000000] | IsPrime(SumOfDivisors(n)) and IsPrime(SumOfDivisors(n^3))];
%o A299153 (PARI) isok(n) = isprime(sigma(n)) && isprime(sigma(n^3)); \\ _Michel Marcus_, Feb 05 2018
%Y A299153 Cf. A000203 (sigma(n)), A055638 (sigma(n^2) is prime), A232444 (sigma(n) and sigma(n^2) are primes), A279094 (the smallest k such that sigma(k^n) is prime), A279096 (sigma(n^3) is prime), A299147 (sigma(n), sigma(n^2) and sigma(n^3) are primes).
%K A299153 nonn
%O A299153 1,1
%A A299153 _Jaroslav Krizek_, Feb 03 2018