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

1,1

Comments

Intersection of A023194 and A279096.

All terms are squares.

Links

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

Example

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

Mathematica

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

Prog

(Magma) [n: n in[1..10000000] | IsPrime(SumOfDivisors(n)) and IsPrime(SumOfDivisors(n^3))]
(PARI) isok(n) = isprime(sigma(n)) && isprime(sigma(n^3)); \\ Michel Marcus, Feb 05 2018

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).

Sequence in context: A115648 A082522 A279096 * A133900 A143480 A230365

Adjacent sequences: A299150 A299151 A299152 * A299154 A299155 A299156

Keyword

nonn

Author

Jaroslav Krizek, Feb 03 2018

Status

approved