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A258777 Number of points of projective spaces on finite fields. 1
1, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 17, 18, 20, 21, 24, 26, 28, 30, 31, 32, 33, 38, 40, 42, 44, 48, 50, 54, 57, 60, 62, 63, 65, 68, 72, 73, 74, 80, 82, 84, 85, 90, 91, 98, 102, 104, 108, 110, 114, 121, 122, 126, 127, 128, 129, 132, 133, 138, 140, 150, 152, 156, 158, 164, 168, 170, 174, 180, 182, 183, 192, 194, 198, 200 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

List of integers of form (p^(k*n) - 1)/(p^k - 1) = sigma_k(p^(n-1)) = sum of d^k over all divisors d of p^(n-1), for some prime p and some positive integers k and n. The cardinality of the field is p^k and the dimension of the space is n-1.

In other words, numbers that are a repunit in at least one base that is a prime power (A246655). - Peter Munn, Oct 21 2020

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Pierre-Emmanuel Caprace, Pierre de la Harpe, Groups with irreducibly unfaithful subsets for unitary representations, arXiv:1807.04992 [math.GR], 2018.

Eric Weisstein's World of Mathematics, Repunit

EXAMPLE

7 = (2^(1*3) - 1)/(2^1 - 1) so 7 is in the sequence. 10 = (3^(2*2) - 1)/(3^2 - 1) so 10 is in the sequence.

MATHEMATICA

max = 200; Join[{1}, Select[{#, DivisorSigma[Range[Max[1, Log[#, max] // Floor]], #]}& /@ Range[2, max], PrimePowerQ[#[[1]]]&][[All, 2]] // Flatten // Union] // Select[#, # <= max&]& (* Jean-Fran├žois Alcover, Jun 24 2015 after Giovanni Resta *)

PROG

(PARI) list(lim)=my(v=List([1]), t); lim\=1; if(lim<2, lim=2); for(k=1, logint(lim - 1, 2), for(n=2, logint(lim*(2^k - 1) + 1, 2)\k, forprime(p=2, , t=(p^(k*n) - 1)/(p^k - 1); if(t>lim, break); listput(v, t)))); Set(v) \\ Charles R Greathouse IV, Jun 24 2015

CROSSREFS

Union of 1, A090503 and (A246655 + 1).

Subsequence of A211347.

Cf. A001231, A246655.

Sequence in context: A026500 A091213 A211347 * A298004 A039238 A299532

Adjacent sequences:  A258774 A258775 A258776 * A258778 A258779 A258780

KEYWORD

nonn,nice

AUTHOR

Matthieu Pluntz, Jun 09 2015

STATUS

approved

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Last modified September 23 02:41 EDT 2021. Contains 347609 sequences. (Running on oeis4.)