login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A299148 a(n) is the smallest number k such that sigma(k) and sigma(k^n) are both primes. 1
2, 2, 4, 2, 25, 2, 262144, 4, 4, 64, 734449, 2, 3100870943041, 9066121, 4, 2, 729, 2, 214355670008317962105386619478205641151753401, 5041, 64, 16, 25, 10651330026288961, 16610312161, 2607021481, 38950081, 1817762776525603445521, 5331481, 2, 2160067977820518171249529658520145004718584607049, 21203610154988994565561 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Sequence b(n) of the smallest numbers m such that sigma(m^k) are all primes for k = 1..n: 2, 2, 4, ... (if fourth term exists, it must be bigger than 10^16).

a(n) is of the form p^e where p, e+1 and e*n+1 are primes. e=1 is possible only in the case p=2. - Robert Israel, Feb 06 2018

LINKS

Robert Israel, Table of n, a(n) for n = 1..79

FORMULA

a(n) >= A279094(n).

EXAMPLE

For n = 3; a(3) = 4 because 4 is the smallest number such that sigma(4) = 7 and sigma(4^3) = 127 are both primes.

MAPLE

f:= proc(n, Nmin, Nmax) local p, e, M, Res;

  M:= Nmax;

  Res:= -1;

  e:= 0;

  do

    e:= nextprime(e+1)-1;

    if 2^e > M then return Res fi;

    if not isprime(e*n+1) then next fi;

    p:= floor(Nmin^(1/e));

    do

      p:= nextprime(p);

      if p^e > M then break fi;

      if e = 1 and p > 2 then break fi;

      if isprime((p^(e+1)-1)/(p-1)) and isprime((p^(e*n+1)-1)/(p-1)) then

        Res:= p^e;

        M:= p^e;

        break

      fi

    od

  od;

end proc:

g:= proc(n) local Nmin, Nmax, v;

  Nmax:= 1;

  do

    Nmin:= Nmax;

    Nmax:= Nmax*10^3;

    v:= f(n, Nmin, Nmax);

    if v > 0 then return v fi;

  od;

end proc:

seq(g(n), n=1..50); # Robert Israel, Feb 06 2018

MATHEMATICA

Array[Block[{k = 2}, While[! AllTrue[DivisorSigma[1, #] & /@ {k, k^#}, PrimeQ], k++]; k] &, 10] (* Michael De Vlieger, Feb 05 2018 *)

PROG

(MAGMA) [Min([n: n in[1..10000000] | IsPrime(SumOfDivisors(n)) and IsPrime(SumOfDivisors(n^k))]): k in [2..12]]

(PARI) a(n) = {my(k=1); while (!(isprime(sigma(k)) && isprime(sigma(k^n))), k++); k; } \\ Michel Marcus, Feb 05 2018

CROSSREFS

Cf. A000203, A279094.

Sequence in context: A102416 A227509 A279094 * A129243 A013551 A252040

Adjacent sequences:  A299145 A299146 A299147 * A299149 A299150 A299151

KEYWORD

nonn

AUTHOR

Jaroslav Krizek, Feb 03 2018

EXTENSIONS

a(13) to a(32) from Robert Israel, Feb 06 2018

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 5 13:26 EST 2019. Contains 329751 sequences. (Running on oeis4.)