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A299153
Numbers k such that sigma(k) and sigma(k^3) are both primes.
2
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.
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: A082522 A279096 A374927 * A133900 A143480 A230365
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Feb 03 2018
STATUS
approved