A299147 -id:A299147 - cp's OEIS frontend

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

Jaroslav Krizek, Feb 03 2018

nonn

Intersection of A023194 and A279096.

All terms are squares.

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

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

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).

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

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

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

cp's OEIS Frontend

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

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