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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[#[]]&][[All, 2]] // Flatten // Union] // Select[#, # <= max&]& (* Jean-François Alcover, Jun 24 2015 after Giovanni Resta *) PROG (PARI) list(lim)=my(v=List(), 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 May 17 04:28 EDT 2022. Contains 353730 sequences. (Running on oeis4.)