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

4, 9, 16, 25, 64, 289, 2401, 7921, 3418801, 19439281, 24730729, 40819321, 52258441, 67848169, 75151561, 76405081, 142396489, 175006441, 185313769, 198443569, 253541929, 352425529, 369062521, 386554921, 414896161, 499477801, 526105969, 684921241, 775678201

Offset: 1

Author

Jaroslav Krizek, Feb 03 2018

Keywords

• nonn

Comments

Intersection of A023194 and A279096.

All terms are squares.

Examples

			4 is in the sequence because sigma(4) = 7 and sigma(4^2) = 31 are both primes.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10203

Crossrefs

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).

Programs

Magma

[n: n in[1..10000000] | IsPrime(SumOfDivisors(n)) and IsPrime(SumOfDivisors(n^3))];

Mathematica

Select[Range[10^4], AllTrue[DivisorSigma[1, #] & /@ {#, #^3}, PrimeQ] &] (* Michael De Vlieger, Feb 05 2018 *)

PARI

isok(n) = isprime(sigma(n)) && isprime(sigma(n^3)); \\ Michel Marcus, Feb 05 2018