A299147 Numbers k such that sigma(k), sigma(k^2) and sigma(k^3) are primes.
4, 64, 289, 253541929, 499477801, 1260747049, 14450203681, 25391466409, 256221229489, 333456586849, 341122579249, 459926756041, 911087431081, 928731181849, 1142288550841, 2880002461249, 2923070670601, 3000305515321, 4103999343889, 4123226708329, 4258977385441
Offset: 1
Keywords
Examples
4 is in the sequence because all sigma(4) = 7, sigma(4^2) = 31 and sigma(4^3) = 127 are primes.
Links
- Chai Wah Wu, Table of n, a(n) for n = 1..12775 (n = 1..997 from Robert G. Wilson v)
Programs
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Magma
[n: n in[1..10000000] | IsPrime(SumOfDivisors(n)) and IsPrime(SumOfDivisors(n^2)) and IsPrime(SumOfDivisors(n^3))];
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Maple
N:= 10^14: # to get all terms <= N Res:= NULL: p:= 1: do p:= nextprime(p); if p^2 > N then break fi; for k from 2 by 2 while p^k <= N do if isprime(k+1) and isprime(2*k+1) and isprime(3*k+1) then q1:= (p^(k+1)-1)/(p-1); q2:= (p^(2*k+1)-1)/(p-1); q3:= (p^(3*k+1)-1)/(p-1); if isprime(q1) and isprime(q2) and isprime(q3) then Res:= Res, p^k; fi fi od od: sort([Res]); # Robert Israel, Feb 22 2018 -
Mathematica
k = 1; A299147 = {}; While[k < 4260000000000, If[Union@ PrimeQ@ DivisorSigma[1, {k, k^2, k^3}] == {True}, AppendTo[A299147, k]]; k++]; A299147 (* Robert G. Wilson v, Feb 10 2018 *)
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PARI
isok(n) = isprime(sigma(n)) && isprime(sigma(n^2)) && isprime(sigma(n^3)); \\ Michel Marcus, Feb 05 2018
Comments