A053183 -id:A053183 - cp's OEIS frontend

A238399 a(n) is the number of primes occurring between A053182(n) and A053183(n) (excluding the endpoints).

2, 3, 7, 55, 255, 478, 663, 984, 1237, 1955, 3021, 3214, 8312, 13519, 38267, 40805, 45400, 47444, 48835, 55269, 56758, 59032, 66067, 92141, 93063, 103620, 106611, 108602, 112713, 140874, 151335, 163314, 178215, 183330, 211350, 235410, 244165, 265160, 275971

Offset: 1

Torlach Rush, Feb 26 2014

nonn

Giovanni Resta, Table of n, a(n) for n = 1..2500

Cf. A053182, A053183

(PrimePi[#^2 + #] - PrimePi[#]) & /@  Select[Prime@Range@500, PrimeQ[#^2 + # + 1] &] (* Giovanni Resta, Feb 27 2014 *)

a(33)-a(39) from Giovanni Resta, Feb 27 2014

A002383 Primes of form k^2 + k + 1.

Original entry on oeis.org

3, 7, 13, 31, 43, 73, 157, 211, 241, 307, 421, 463, 601, 757, 1123, 1483, 1723, 2551, 2971, 3307, 3541, 3907, 4423, 4831, 5113, 5701, 6007, 6163, 6481, 8011, 8191, 9901, 10303, 11131, 12211, 12433, 13807, 14281, 17293, 19183, 20023, 20593, 21757, 22651, 23563

Offset: 1

N. J. A. Sloane

Also primes p such that 4p-3 is square. - Giovanni Teofilatto, Sep 07 2005
Also these primes are sums of 1 and some consecutive even numbers starting at 2; e.g., 31 = 1+2+4+6+8+10. - Labos Elemer, Apr 15 2003
Also primes of form n^2 - n + 1 (Prime central polygonal numbers, A002061). - Zak Seidov, Jan 26 2006
Also primes which are of the form TriangularNumber(n) + TriangularNumber(n+2): 7 = 1+6, 13 = 3+10, 31 = 10+21, 43 = 15+28, 73 = 28+45, ... - Vladimir Joseph Stephan Orlovsky, Apr 03 2009
It is not known whether there are infinitely many primes of the form n^2+n+1. See Rose reference. - Daniel Tisdale, Jun 27 2009
These numbers when >= 7 are prime repunits 111_n in a base n >= 2, so except for 3, they are all Brazilian primes belonging to A085104. (See Links "Les nombres brésiliens", Sections V.4 - V.5.) A002383 is generated by A002384 which lists the bases n of 111_n. A002383 = A053183 Union A185632. - Bernard Schott, Dec 22 2012
Conjecture: the set of these numbers, except 3, is the intersection of sets A085104 and A059055. See A225148. - Thomas Ordowski, May 02 2013
For a(n)>13, the fractional part of square root of a(n) starts with digit 5 (see A034101). - Charles Kusniec, Sep 06 2022

D. H. Lehmer, Guide to Tables in the Theory of Numbers. Bulletin No. 105, National Research Council, Washington, DC, 1941, p. 46.
L. Poletti, Le serie dei numeri primi appartenente alle due forme quadratiche (A) n^2+n+1 e (B) n^2+n-1 per l'intervallo compreso entro 121 milioni, e cioè per tutti i valori di n fino a 11000, Atti della Reale Accademia Nazionale dei Lincei, Memorie della Classe di Scienze Fisiche, Matematiche e Naturali, s. 6, v. 3 (1929), pages 193-218.
H. E. Rose, A Course in Number Theory, Clarendon Press, 1988, p. 217.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Zak Seidov, Table of n, a(n) for n = 1..10751
Cody S. Hansen and Pace P. Nielsen, Prime factors of phi3(x) of the same form, arXiv:2204.08971 [math.NT], 2022.
Bernard Schott, Les nombres brésiliens, Quadrature, no. 76, avril-juin 2010, pages 30-38; included here with permission from the editors of Quadrature.

Cf. A002384, A088503, A110284, A085104.
Cf. A237037, A237038, A237039, A237040 (from semiprimes of form n^3 + 1).
See also A034101.

[ a: n in [1..100] | IsPrime(a) where a is n^2+n+1 ]; // Wesley Ivan Hurt, Jun 16 2014

select(isprime, [j^2+j+1$j=1..200])[];  # Alois P. Heinz, Apr 20 2022

Select[Table[n^2+n+1, {n,250}], PrimeQ] (* Harvey P. Dale, Mar 23 2012 *)

list(lim)=select(n->isprime(n),vector((sqrt(4*lim-3)-1)\2,k,k^2+k+1)) \\ Charles R Greathouse IV, Jul 25 2011

from sympy import isprime
print(list(filter(isprime, (n**2 + n + 1 for n in range(150))))) # Michael S. Branicky, Apr 20 2022

a(n) = A002384(n)^2 + A002384(n) + 1 = (A088503(n-1)^2 + 3)/4 = (A110284(n) + 3)/4. - Ray Chandler, Sep 07 2005

Extended by Ray Chandler, Sep 07 2005

A001001 Number of sublattices of index n in generic 3-dimensional lattice.

Original entry on oeis.org

1, 7, 13, 35, 31, 91, 57, 155, 130, 217, 133, 455, 183, 399, 403, 651, 307, 910, 381, 1085, 741, 931, 553, 2015, 806, 1281, 1210, 1995, 871, 2821, 993, 2667, 1729, 2149, 1767, 4550, 1407, 2667, 2379, 4805, 1723, 5187, 1893, 4655, 4030, 3871, 2257, 8463, 2850, 5642, 3991, 6405, 2863

Offset: 1

N. J. A. Sloane

These sublattices are in 1-1 correspondence with matrices
[a b d]
[0 c e]
[0 0 f]
with acf = n, b = 0..c-1, d = 0..f-1, e = 0..f-1. The sublattice is primitive if gcd(a,b,c,d,e,f) = 1.
Total area of all distinct rectangles whose side lengths are divisors of n, and whose length is an integer multiple of the width. - Wesley Ivan Hurt, Aug 23 2020

Richard P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 5.13(d), pp. 76 and 113.

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe)
Michael Baake, Solution of the coincidence problem in dimensions d <= 4, in R. V. Moody, ed., Math. of Long-Range Aperiodic Order, Kluwer 1997, pp. 9-44.; arXiv:math/0605222 [math.MG], 2006.
M. Baake and N. Neumarker, A Note on the Relation Between Fixed Point and Orbit Count Sequences, JIS 12 (2009) 09.4.4, Section 3.
J. Liouville, Théorème concernant les sommes de diviseurs des nombres, Journal de mathématiques pures et appliquées 2e série, tome 2 (1857), p. 56.
V. A. Liskovets and A. Mednykh, Enumeration of subgroups in the fundamental groups of orientable circle bundles over surfaces, Commun. in Algebra, 28, No. 4 (2000), 1717-1738.
Y. Puri and T. Ward, Arithmetic and growth of periodic orbits, J. Integer Seqs., Vol. 4 (2001), #01.2.1.
J. S. Rutherford, The enumeration and symmetry-significant properties of derivative lattices, Act. Cryst. (1992) A48, 500-508
J. S. Rutherford, The enumeration and symmetry-significant properties of derivative lattices II, Acta Cryst. A49 (1993), 293-300. [_N. J. A. Sloane_, Mar 14 2009]
Tad White, Counting Free Abelian Actions, arXiv:1304.2830 [math.CO], 2013.
Index entries for sequences related to sublattices.

Column 3 of A160870.
Cf. A060983, A064987 (Mobius transform).
Cf. A061256, A226313, A301777.
Primes in this sequence are in A053183.
Cf. A038991, A038992, A038993, A038994, A038995, A038996, A038997, A038998, A038999.

a001001 n = sum [sum [k * (if k `mod` l == 0 then l else 0) | k <- [1..n], n `mod` k == 0 ] | l <- [1..n]]
a = [ a001001 n | n <- [1..53]]
putStrLn $ concat $ map (++ ", ") (map show a) -- Miles Wilson, Apr 04 2025

nmax := 100:
L12 := [seq(1,i=1..nmax) ];
L27 := [seq(i,i=1..nmax) ];
L290 := [seq(i^2,i=1..nmax) ];
DIRICHLET(L12,L27) ;
DIRICHLET(%,L290) ; # R. J. Mathar, Sep 25 2017

a[n_] := Sum[ d*DivisorSigma[1, d], {d, Divisors[n]}]; Table[ a[n], {n, 1, 42}] (* Jean-François Alcover, Jan 20 2012, after Vladeta Jovovic *)
f[p_, e_] := Product[(p^(e + k) - 1)/(p^k - 1), {k, 1, 2}]; a[1] = 1; a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 100] (* Amiram Eldar, Aug 29 2019 *)

N=17; default(seriesprecision,N); x=z+O(z^(N+1))
c=sum(j=1,N,j*x^j);
t=1/prod(j=1,N, eta(x^(j))^j)
t=log(t)
t=serconvol(t,c)
Vec(t)
/* Joerg Arndt, May 03 2008 */

a(n)=sumdiv(n,d, d * sumdiv(d,t, t ) );  /* Joerg Arndt, Oct 07 2012 */

a(n)=sumdivmult(n,d, sigma(d)*d) \\ Charles R Greathouse IV, Sep 09 2014

If n = Product p^m, a(n) = Product (p^(m + 1) - 1)(p^(m + 2) - 1)/(p - 1)(p^2 - 1). Or, a(n) = Sum_{d|n} sigma(n/d)*d^2, Dirichlet convolution of A000290 and A000203.
a(n) = Sum_{d|n} d*sigma(d). - Vladeta Jovovic, Apr 06 2001
Multiplicative with a(p^e) = ((p^(e+1)-1)(p^(e+2)-1))/((p-1)(p^2-1)). - David W. Wilson, Sep 01 2001
Dirichlet g.f.: zeta(s)*zeta(s-1)*zeta(s-2).
L.g.f.: -log(Product_{k>=1} (1 - x^k)^sigma(k)) = Sum_{n>=1} a(n)*x^n/n. - Ilya Gutkovskiy, May 23 2018
a(n) = Sum_{d1|n, d2|n, d1|d2} d1*d2. - Wesley Ivan Hurt, Aug 23 2020
Sum_{k=1..n} a(k) ~ c * n^3, where c = Pi^2*zeta(3)/18 = 0.659101... . - Amiram Eldar, Oct 19 2022
G.f.: Sum_{k>=1} Sum {l>=1} k*l^2*x^(k*l - 1)/(1 - x^(k*l)). - Miles Wilson, Apr 04 2025

A053182 Primes p such that p^2 + p + 1 is prime.

Original entry on oeis.org

2, 3, 5, 17, 41, 59, 71, 89, 101, 131, 167, 173, 293, 383, 677, 701, 743, 761, 773, 827, 839, 857, 911, 1091, 1097, 1163, 1181, 1193, 1217, 1373, 1427, 1487, 1559, 1583, 1709, 1811, 1847, 1931, 1973, 2129, 2273, 2309, 2339, 2411, 2663, 2729, 2789, 2957

Offset: 1

Enoch Haga, Mar 01 2000

Roger Horn computed the first 776 terms of this sequence around 1961 to test (with Paul Bateman) their conjecture on the density of simultaneous primes in polynomials. - Charles R Greathouse IV, Apr 05 2011
Starting with a(3)=5 all terms are of the form 6k-1, k in A147683. - Zak Seidov, Nov 10 2008
Primes p such that the sum of divisors of p^2 (sigma(p^2) = A000203(p^2) = p^2+p+1) is prime. - Claudio Meller, Apr 07 2011
The generated prime numbers p^2 + p + 1 are exactly A053183. - Bernard Schott, Dec 20 2012
Positive squarefree k such that the sum of divisors of k^2 is prime. - Peter Munn, Feb 02 2018

Jon E. Schoenfield, Table of n, a(n) for n = 1..10000 (first 2650 terms from M. F. Hasler).
Paul T. Bateman and Roger A. Horn, A heuristic asymptotic formula concerning the distribution of prime numbers, Math. Comp. 16 (1962), 363-367.
Paolo Santonastaso and Ferdinando Zullo, Linearized trinomials with maximum kernel, arXiv:2012.14861 [math.NT], 2020.

Cf. A053184, A065508, A091567, A147683, A188596.

[p: p in PrimesUpTo(10000) | IsPrime(p^2+p+1)]; // Vincenzo Librandi, Aug 06 2010

Select[Prime[Range[427]], PrimeQ[#^2+#+1]&] (* Bruno Berselli, Nov 08 2011 *)

isA053182(n)=isprime(n) && isprime(n^2+n+1)  \\ Michael B. Porter, Apr 23 2010

c=0; forprime(p=1,default(primelimit), isprime(p^2+p+1) & write("/tmp/b053182.txt",c++," "p))  \\ M. F. Hasler, Apr 07 2011

List changed to cross-reference by Franklin T. Adams-Watters, May 12 2010

A023195 Prime numbers that are the sum of the divisors of some n.

Original entry on oeis.org

3, 7, 13, 31, 127, 307, 1093, 1723, 2801, 3541, 5113, 8011, 8191, 10303, 17293, 19531, 28057, 30103, 30941, 86143, 88741, 131071, 147073, 292561, 459007, 492103, 524287, 552793, 579883, 598303, 684757, 704761, 732541, 735307, 797161, 830833, 1191373

Offset: 1

David W. Wilson

nonn

If n > 2 and sigma(n) is prime, then n must be an even power of a prime number. For example, 1093 = sigma(3^6). - T. D. Noe, Jan 20 2004
All primes of the form 2^n-1 (Mersenne primes) are in the sequence because if n is a natural number then sigma(2^(n-1)) = 2^n-1. So A000668 is a subsequence of this sequence. If sigma(n) is prime then n is of the form p^(q-1) where both p & q are prime (the proof is easy). - Farideh Firoozbakht, May 28 2005
Primes of the form 1 + p + p^2 + ... + p^k where p is prime.
If n = sigma(p^k) is in the sequence, then k+1 is prime. - Franklin T. Adams-Watters, Dec 19 2011
Primes that are a repunit in a prime base. - Franklin T. Adams-Watters, Dec 19 2011.
Except for 3, these primes are particular Brazilian primes belonging to A085104. These prime numbers are also Brazilian primes of the form (p^x - 1)/(p^y - 1), p prime, belonging to A003424, with here x is prime, and y = 1. [See section V.4 of Quadrature article in Links.] - Bernard Schott, Dec 25 2012
From Bernard Schott, Dec 25 2012: (Start)
Others subsequences of this sequence:
  A053183 for 111_p = p^2 + p + 1 when p is prime.
  A190527 for 11111_p =  p^4 + p^3 + p^2 + p + 1 when p is prime.
  A194257 for 1111111_p = p^6 + p^5 + p^4 + p^3 + p^2 + p + 1 when p is prime. (End)
Subsequence of primes from A002191. - Michel Marcus, Jun 10 2014

			307 = 1 + 17 + 17^2; 307 and 17 are primes.

David W. Wilson, Table of n, a(n) for n = 1..10000
Bernard Schott, Les nombres brésiliens, Quadrature, no. 76, avril-juin 2010, pages 30-38; included here with permission from the editors of Quadrature.

Intersection of A002191 and A000040.

Cf. A000203, A000668, A023194 (the n that produce these primes), A053696, A085104, A003424, A053183, A190527, A194257.

t={3}; lim=10^9; n=1; While[p=Prime[n]; k=2; s=1+p+p^2; sHarvey P. Dale, Jun 18 2022 *)

upto(lim)=my(v=List([3]),t); forprime(p=2,solve(x=1,lim^(1/4), x^4+x^3+x^2+x+1-lim), forprime(e=5,1+log(lim)\log(p), if(isprime(t=sigma(p^(e-1))) && t<=lim, listput(v,t)))); forprime(p=2, solve(x=1,lim^(1/2),x^2+x+1-lim), if(isprime(t=p^2+p+1), listput(v,t))); vecsort(Vec(v),,8) \\ Charles R Greathouse IV, Dec 20 2011

from sympy import isprime, divisor_sigma
A023195_list = sorted(set([3]+[n for n in (divisor_sigma(d**2) for d in range(1,10**4)) if isprime(n)])) # Chai Wah Wu, Jul 23 2016

A065405 Composite numbers k such that the sum of the divisors of k^2 is a prime.

Original entry on oeis.org

4, 8, 27, 49, 64, 125, 169, 256, 289, 512, 529, 729, 841, 1849, 2197, 3125, 4913, 5329, 6241, 6889, 15625, 16129, 29791, 32768, 37249, 51529, 57121, 69169, 76729, 113569, 117649, 128881, 139129, 157609, 192721, 208849, 226981, 229441, 253009

Offset: 1

Labos Elemer, Nov 06 2001

nonn

All these composite numbers k should be prime powers because if k=a*b with gcd(a,b)=1, then sigma(aabb) = sigma(aa)*sigma(bb) cannot be a prime; 46 of the 236 prime powers below 1000000 are here.

Amiram Eldar, Table of n, a(n) for n = 1..500 (terms 1..70 from Harry J. Smith)

Cf. A062700, A000203, A065403, A065404, A053182, A053183, A028982.

Select[ Range[3 10^5], ! PrimeQ[ # ] && PrimeQ[ DivisorSigma[1, #^2]] & ]

isok(k) = { !isprime(k) && isprime(sigma(k^2)) } \\ Harry J. Smith, Oct 18 2009

sigma(a(n)^2) = sigma(A065404(n)) = A065403(n) is prime.

A185632 Primes of the form n^2 + n + 1 where n is nonprime.

Original entry on oeis.org

3, 43, 73, 157, 211, 241, 421, 463, 601, 757, 1123, 1483, 2551, 2971, 3307, 3907, 4423, 4831, 5701, 6007, 6163, 6481, 8191, 9901, 11131, 12211, 12433, 13807, 14281, 19183, 20023, 20593, 21757, 22651, 23563, 24181, 26083, 26407, 27061, 28393, 31153, 35533

Offset: 1

Bernard Schott, Dec 18 2012

nonn

These are the primes associated with A182253.
All these numbers are in A002383 but not in A053183.
All the numbers n^2 + n + 1 = 111_n with n >= 2 are by definition Brazilian numbers: A125134. See Links: "Les nombres brésiliens" - Section V.5 page 35.

Harvey P. Dale, Table of n, a(n) for n = 1..1000
Bernard Schott, Les nombres brésiliens, Quadrature, no. 76, avril-juin 2010, pages 30-38.
Bernard Schott, Les nombres brésiliens, Reprinted from Quadrature, no. 76, avril-juin 2010, pages 30-38, included here with permission from the editors of Quadrature.

Cf. A002383, A002384, A053182, A053183, A182253.

Cf. A085104, A125134.

Select[Table[If[PrimeQ[n],Nothing,n^2+n+1],{n,200}],PrimeQ] (* Harvey P. Dale, Apr 02 2023 *)

lista(nn) = {for (n = 1, nn, if (! isprime(n) && isprime(p = n^2 + n + 1), print1(p, ", ");););} \\ Michel Marcus, Sep 04 2013

A285017 Primes of the form 1 + n + n^2 + n^3 + ... + n^k, n > 1, k > 1 where n is not prime.

Original entry on oeis.org

43, 73, 157, 211, 241, 421, 463, 601, 757, 1123, 1483, 2551, 2971, 3307, 3907, 4423, 4831, 5701, 6007, 6163, 6481, 8191, 9901, 11131, 12211, 12433, 13807, 14281, 19183, 20023, 20593, 21757, 22621, 22651, 23563, 24181, 26083, 26407, 27061, 28393, 31153, 35533

Offset: 1

Bernard Schott, Apr 08 2017

nonn

These numbers are Brazilian primes belonging to A085104.
Brazilian primes with n prime are A023195, except 3 which is not Brazilian.
A085104 = This sequence Union { A023195 \ number 3 }.
k + 1 is necessarily prime, but that's not sufficient: 1 + 10 + 100 = 111.
Most of these terms come from A185632 which are prime numbers 111_n with n no prime, the first other term is 22621 = 11111_12, the next one is 245411 = 11111_22.
Number of terms < 10^k: 0, 2, 9, 23, 64, 171, 477, 1310, 3573, 10098, ..., . - Robert G. Wilson v, Apr 15 2017

			157 = 12^2 + 12 + 1 = 111_12 is prime and 12 is composite.

Chai Wah Wu, Table of n, a(n) for n = 1..10000 (terms 1..1310 from Robert G. Wilson v)
Bernard Schott, Les nombres brésiliens, Reprinted from Quadrature, no. 76, April-June 2010, pages 30-38, included here with permission from the editors of Quadrature.

Cf. A002383, A023195, A053183, A053696, A085104, A088548, A088550, A185632, A190527, A194257.

N:= 40000: # to get all terms <= N
res:= NULL:
for k from 2 to ilog2(N) do if isprime(k) then
  for n from 2 do
    p:= (n^(k+1)-1)/(n-1);
    if p > N then break fi;
    if isprime(p) and not isprime(n) then res:= res, p fi
od fi od:
res:= {res}:
sort(convert(res,list)); # Robert Israel, Apr 14 2017

mx = 36000; g[n_] := Select[Drop[Accumulate@Table[n^ex, {ex, 0, Log[n, mx]}], 2], PrimeQ]; k = 1; lst = {}; While[k < Sqrt@mx, If[CompositeQ@k, AppendTo[lst, g@k]; lst = Sort@Flatten@lst]; k++]; lst (* Robert G. Wilson v, Apr 15 2017 *)

isok(n) = {if (isprime(n), forcomposite(b=2, n, d = digits(n, b); if ((#d > 2) && (vecmin(d) == 1) && (vecmax(d)== 1), return(1)););); return(0);} \\ Michel Marcus, Apr 09 2017

A285017_vec(n)={my(h=vector(n,i,1),y,c,z=4,L:list);L=List();forprime(x=3,,forcomposite(m=z,x-1,y=digits(x,m);if((y==h[1..#y])&&2<#y,listput(L,x);z=m;if(c++==n,return(Vec(L))))))} \\ R. J. Cano, Apr 18 2017

A065404 Squares of composite numbers k such that sigma(k) (sum of divisors of k, A000203) is a prime.

Original entry on oeis.org

16, 64, 729, 2401, 4096, 15625, 28561, 65536, 83521, 262144, 279841, 531441, 707281, 3418801, 4826809, 9765625, 24137569, 28398241, 38950081, 47458321, 244140625, 260144641, 887503681, 1073741824, 1387488001, 2655237841

Offset: 1

Labos Elemer, Nov 06 2001

nonn

			46 cases below 10^12; for M a Mersenne prime, (M+1)/2 is here: M=8191, 4096=(M+1)/2.

Amiram Eldar, Table of n, a(n) for n = 1..500 (terms 1..100 from Harry J. Smith)

Cf. A062700, A000203 (sigma), A065403, A065405, A053182, A053183, A028982.

{ n=0; for (m=1, 10^9, if (isprime(m), next); x=sigma(m^2); if (isprime(x), write("b065404.txt", n++, " ", m^2); if (n==100, return)) ) } \\ Harry J. Smith, Oct 18 2009

sigma(a(n)) = A065403(n).

A182253 Nonprime numbers n such that n^2 + n + 1 is prime.

Original entry on oeis.org

1, 6, 8, 12, 14, 15, 20, 21, 24, 27, 33, 38, 50, 54, 57, 62, 66, 69, 75, 77, 78, 80, 90, 99, 105, 110, 111, 117, 119, 138, 141, 143, 147, 150, 153, 155, 161, 162, 164, 168, 176, 188, 189, 192, 194, 203, 206, 209, 215, 218, 231, 236, 245, 246, 266, 272, 278

Offset: 1

Bernard Schott, Dec 18 2012

nonn

All these numbers are in A002384 but not in A053182.
The generated prime numbers n^2 + n + 1 are in A185632.
All the generated numbers n^2 + n + 1 = 111_n are by definition Brazilian numbers: A125134. See Links: "Les nombres brésiliens" - Section V.5 page 35.

Michael De Vlieger, Table of n, a(n) for n = 1..10000
Bernard Schott, Les nombres brésiliens, Quadrature, no. 76, avril-juin 2010, pages 30-38; included here with permission from the editors of Quadrature.

Cf. A002383, A002384, A053182, A053183, A085104, A125134, A185632.

Select[Range@ 280, And[! PrimeQ@ #, PrimeQ[#^2 + # + 1]] &] (* Michael De Vlieger, Jul 30 2017 *)

isok(n) = ! isprime(n) && isprime(n^2 + n + 1); \\ Michel Marcus, Sep 04 2013

cp's OEIS Frontend

A238399 a(n) is the number of primes occurring between A053182(n) and A053183(n) (excluding the endpoints).

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A002383 Primes of form k^2 + k + 1.

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A001001 Number of sublattices of index n in generic 3-dimensional lattice.

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A053182 Primes p such that p^2 + p + 1 is prime.

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A023195 Prime numbers that are the sum of the divisors of some n.

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A065405 Composite numbers k such that the sum of the divisors of k^2 is a prime.

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A185632 Primes of the form n^2 + n + 1 where n is nonprime.

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