A001358 -id:A001358 - cp's OEIS frontend

A078972 Brilliant numbers: semiprimes (products of two primes, A001358) whose prime factors have the same number of decimal digits.

4, 6, 9, 10, 14, 15, 21, 25, 35, 49, 121, 143, 169, 187, 209, 221, 247, 253, 289, 299, 319, 323, 341, 361, 377, 391, 403, 407, 437, 451, 473, 481, 493, 517, 527, 529, 533, 551, 559, 583, 589, 611, 629, 649, 667, 671, 689, 697, 703, 713, 731, 737, 767, 779, 781

Offset: 1

Jason Earls, Jan 12 2003

"Brilliant numbers, as defined by Peter Wallrodt, are numbers with two prime factors of the same length (in decimal notation). These numbers are generally used for cryptographic purposes and for testing the performance of prime factoring programs." [Alpern]
Up to 10^8 the approximate sum of reciprocals is ~1.232884485... - Jason Earls, Oct 15 2010
Let f(n) = a(n) - floor(sqrt(a(n)))^2, or how much larger a(n) is than the largest square number <= a(n). Then f(n) is odd for all even squares, and even for all odd squares where n > 5. See "Ulam spiral" in links. - Christian N. K. Anderson, Jun 12 2013

			1711 = 29*59 is in the sequence since both of its factors have two digits.

P. D. James, The Private Patient, Knopf, NY, 2008, p. 192. (from N. J. A. Sloane, Aug 27 2009)

T. D. Noe, Table of n, a(n) for n = 1..10537
Dario Alpern, Brilliant Numbers.
Christian N. K. Anderson, Ulam Spiral of n=1..3000.

Cf. A001358, A085647, A084126, A084127, A055642, A085721, A376703, A376704.

Row 2 of A376738.

import Data.Function (on)
a078972 n = a078972_list !! (n-1)
a078972_list = filter brilliant a001358_list where
   brilliant x = (on (==) a055642) p (x `div` p) where p = a020639 x
-- Reinhard Zumkeller, Nov 10 2013, Mar 22 2014

fQ[n_] := Block[{fi = FactorInteger@n}, Plus @@ Last /@ fi == 2 && Floor[ Log[10, fi[[1, 1]] ]] == Floor[ Log[10, fi[[ -1, 1]] ]]]; Select[ Range@792, fQ@# &] (* Robert G. Wilson v, May 26 2006 *)
Select[Range[800],PrimeOmega[#]==2&&Length[Union[IntegerLength[FactorInteger[#][[;;,1]]]]]==1&] (* Harvey P. Dale, Jan 24 2025 *)
Select[Range@1000, Differences@IntegerLength@Flatten@(ConstantArray@@#&/@FactorInteger[#]) == {0} &] (* Hans Rudolf Widmer, Oct 25 2022 *)
dlist2[d_] := Union[Times @@@ Tuples[Prime[Range[PrimePi[10^(d-1)] + 1, PrimePi[10^d]]], 2]]; (* Generates terms with d-digits prime factors *)
Flatten[Array[dlist2, 2]] (* Paolo Xausa, Oct 05 2024 *)

is(n)=my(f=factor(n));(#f[,1]==1 && f[1,2]==2) || (#f[,1]==2 && f[1,2]==1 && f[2,2]==1 && #Str(f[1,1])==#Str(f[2,1])) \\ Charles R Greathouse IV, Jun 16 2011

from sympy import sieve
A078972 = []
for n in range(3):
    pr = list(sieve.primerange(10**n,10**(n+1)))
    for i,p in enumerate(pr):
        for q in pr[i:]:
            A078972.append(p*q)
A078972 = sorted(A078972)
# Chai Wah Wu, Aug 26 2014

a(n) = A239585(n) * A239586(n). - Reinhard Zumkeller, Mar 22 2014

Edited by N. J. A. Sloane, Aug 27 2009

A338898 Concatenated sequence of prime indices of semiprimes (A001358).

Original entry on oeis.org

1, 1, 1, 2, 2, 2, 1, 3, 1, 4, 2, 3, 2, 4, 1, 5, 3, 3, 1, 6, 2, 5, 1, 7, 3, 4, 1, 8, 2, 6, 1, 9, 4, 4, 2, 7, 3, 5, 2, 8, 1, 10, 1, 11, 3, 6, 2, 9, 1, 12, 4, 5, 1, 13, 3, 7, 1, 14, 2, 10, 4, 6, 2, 11, 1, 15, 3, 8, 1, 16, 2, 12, 3, 9, 1, 17, 4, 7, 5, 5, 1, 18, 2

Offset: 1

Gus Wiseman, Nov 15 2020

This is a triangle with two columns and weakly increasing rows, namely {A338912(n), A338913(n)}.

A semiprime is a product of any two prime numbers. A prime index of n is a number m such that the m-th prime number divides n. The multiset of prime indices of n is row n of A112798.

			The sequence of semiprimes together with their prime indices begins:
      4: {1,1}     46: {1,9}      91: {4,6}     141: {2,15}
      6: {1,2}     49: {4,4}      93: {2,11}    142: {1,20}
      9: {2,2}     51: {2,7}      94: {1,15}    143: {5,6}
     10: {1,3}     55: {3,5}      95: {3,8}     145: {3,10}
     14: {1,4}     57: {2,8}     106: {1,16}    146: {1,21}
     15: {2,3}     58: {1,10}    111: {2,12}    155: {3,11}
     21: {2,4}     62: {1,11}    115: {3,9}     158: {1,22}
     22: {1,5}     65: {3,6}     118: {1,17}    159: {2,16}
     25: {3,3}     69: {2,9}     119: {4,7}     161: {4,9}
     26: {1,6}     74: {1,12}    121: {5,5}     166: {1,23}
     33: {2,5}     77: {4,5}     122: {1,18}    169: {6,6}
     34: {1,7}     82: {1,13}    123: {2,13}    177: {2,17}
     35: {3,4}     85: {3,7}     129: {2,14}    178: {1,24}
     38: {1,8}     86: {1,14}    133: {4,8}     183: {2,18}
     39: {2,6}     87: {2,10}    134: {1,19}    185: {3,12}

A112798 restricted to rows of length 2 gives this triangle.
A115392 is the row number for the first appearance of each positive integer.
A176506 gives row differences.
A338899 is the squarefree version.
A338912 is column 1.
A338913 is column 2.
A001221 counts a number's distinct prime indices.
A001222 counts a number's prime indices.
A001358 lists semiprimes.
A004526 counts 2-part partitions.
A006881 lists squarefree semiprimes.
A037143 lists primes and semiprimes.
A046315 and A100484 list odd and even semiprimes.
A046388 and A100484 list odd and even squarefree semiprimes.
A065516 gives first differences of semiprimes.
A084126 and A084127 give the prime factors of semiprimes.
A270650 and A270652 give the prime indices of squarefree semiprimes.
A320655 counts factorizations into semiprimes.
Cf. A056239, A101048, A320892, A320912, A338900, A338901, A338904, A338906, A338907, A338910, A338911.

primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
Join@@primeMS/@Select[Range[100],PrimeOmega[#]==2&]

A072000 Number of semiprimes (A001358) <= n.

Original entry on oeis.org

0, 0, 0, 1, 1, 2, 2, 2, 3, 4, 4, 4, 4, 5, 6, 6, 6, 6, 6, 6, 7, 8, 8, 8, 9, 10, 10, 10, 10, 10, 10, 10, 11, 12, 13, 13, 13, 14, 15, 15, 15, 15, 15, 15, 15, 16, 16, 16, 17, 17, 18, 18, 18, 18, 19, 19, 20, 21, 21, 21, 21, 22, 22, 22, 23, 23, 23, 23, 24, 24, 24, 24, 24, 25, 25, 25, 26

Offset: 1

Benoit Cloitre, Jun 19 2002

Number of k <= n such that bigomega(k) = 2.

A. Hildebrand, On the number of prime factors of an integer, in Ramanujan Revisited (Urbana-Champaign, Ill., 1987), pp. 167-185, Academic Press, Boston, MA, 1988.
E. Landau, Handbuch der Lehre von der Verteilung der Primzahlen, vol. 1, Teubner, Leipzig, 1909; third edition : Chelsea, New York (1974).
G. Tenenbaum, Introduction à la théorie analytique et probabiliste des nombres, p. 203, Publications de l'Institut Cartan, 1990.

Daniel Forgues, Table of n, a(n) for n = 1..40882
Dragos Crisan and Radek Erban, On the counting function of semiprimes, arXiv:2006.16491 [math.NT], 2020.
E. Landau, Handbuch der Lehre von der Verteilung der Primzahlen, vol. 1 and vol. 2, Leipzig, Berlin, B. G. Teubner, 1909.
Eric Weisstein's World of Mathematics, Semiprime

Cf. A000720, A001358, A066265, A064911.

A072000 := proc(n) local sp,t ; sp := 0 ; for t from 1 to n do if numtheory[bigomega](t) = 2 then sp := sp+1 ; fi ; od ; sp ; end proc: # R. J. Mathar, Jun 10 2007

semiPrimePi[n_] := Sum[ PrimePi[n/Prime@i] -i + 1, {i, PrimePi@Sqrt@n}]; Array[semiPrimePi, 78] (* Robert G. Wilson v, Jan 03 2006 *)
(* If version >= 7 *) a[n_] := Select[Range[n], PrimeOmega[#] == 2 &] // Length; Table[a[n], {n, 1, 77}] (* Jean-François Alcover, Jun 29 2013 *)
Accumulate[Table[If[PrimeOmega[n]==2,1,0],{n,100}]] (* Harvey P. Dale, Jun 14 2014 *)

for(n=1,100,print1(sum(i=1,n,if(bigomega(i)-2,0,1)),","))

a(n)=my(s=0,i=0); forprime(p=2, sqrt(n), s+=primepi(n\p); i++); s - i * (i-1)/2 \\ Charles R Greathouse IV, Apr 21 2011

from math import isqrt
from sympy import primepi, prime
def A072000(n): return int(sum(primepi(n//prime(k))-k+1 for k in range(1,primepi(isqrt(n))+1))) # Chai Wah Wu, Jul 23 2024

Let PrimePi(x) denote the number of primes <= x (cf. A000720). Then 2*a(n) = Sum_{ primes p <= n/2 } PrimePi(n/p) + PrimePi(sqrt(n)). [Landau, p. 211]
Let PrimePi(x) denote the number of primes <= x (cf. A000720). Then a(n) = Sum_{i=1..PrimePi(sqrt(n))} (PrimePi(n/prime(i)) - i + 1). - Robert G. Wilson v, Feb 07 2006
a(n) = card { x <= n : bigomega(x) = 2 }.
Asymptotically a(n) ~ n*log(log(n))/log(n). [Landau, p. 211]
Let A be a positive integer. Then card { x <= n : bigomega(x) = A } ~ (n/log(n))*log(log(n))^(A-1)/(A-1)! [Landau, p. 211]
a(n) = A072613(n) + A056811(n). - R. J. Mathar, Jun 10 2007
a(n) = Sum_{i=1..n} A064911(i). - Jonathan Vos Post, Dec 30 2007
a(n)*A064911(n) = A174956(n). - Reinhard Zumkeller, Apr 03 2010

Edited by Robert G. Wilson v, Feb 15 2006

A085724 Numbers k such that 2^k - 1 is a semiprime (A001358).

Original entry on oeis.org

4, 9, 11, 23, 37, 41, 49, 59, 67, 83, 97, 101, 103, 109, 131, 137, 139, 149, 167, 197, 199, 227, 241, 269, 271, 281, 293, 347, 373, 379, 421, 457, 487, 523, 727, 809, 881, 971, 983, 997, 1061, 1063

Offset: 1

Jason Earls, Jul 20 2003

Subsequence of A000430. Apart from 4, 9, and 49 composites in this sequence are greater than 1.9e7. - Charles R Greathouse IV, Jun 05 2013
1427 and 1487 are also terms. 1277 is the only remaining unknown below them. - Charles R Greathouse IV, Jun 05 2013
Among the known terms only 11, 23, 83 and 131 are in A002515, that is, they are the only known values for n such that (2^n - 1)/(2*n + 1) is prime. - Jianing Song, Jan 22 2019
Either a(n) is a prime, or the square of a Mersenne prime exponent. - M. F. Hasler, Jun 23 2025

			11 is a member because 2^11 - 1 = 23*89.

J. Earls, Mathematical Bliss, Pleroma Publications, 2009, pages 56-60. ASIN: B002ACVZ6O [From Jason Earls, Nov 22 2009]
J. Earls, "Cole Semiprimes," Mathematical Bliss, Pleroma Publications, 2009, pages 56-60. ASIN: B002ACVZ6O [From Jason Earls, Nov 25 2009]

S. S. Wagstaff, Jr., The Cunningham Project
Eric Weisstein's World of Mathematics, Mersenne Number
Eric Weisstein's World of Mathematics, Semiprime

Cf. A092558, A092559, A092561, A092562.

SemiPrimeQ[n_]:=(n>1) && (2==Plus@@(Transpose[FactorInteger[n]][[2]])); Select[Range[100],SemiPrimeQ[2^#-1]&] (Noe)
Select[Range[1100],PrimeOmega[2^#-1]==2&] (* Harvey P. Dale, Feb 18 2018 *)
Select[Range[250], Total[Last /@ FactorInteger[2^# - 1, 3]] == 2 &] (* Eric W. Weisstein, Jul 28 2022 *)

issemi(n)=bigomega(n)==2
is(n)=if(isprime(n), issemi(2^n-1), my(q); isprimepower(n,&q)==2 && ispseudoprime(2^q-1) && ispseudoprime((2^n-1)/(2^q-1))) \\ Charles R Greathouse IV, Jun 05 2013

More terms from Zak Seidov, Feb 27 2004
More terms from Cunningham project, Mar 23 2004
More terms from the Cunningham project sent by Robert G. Wilson v and T. D. Noe, Feb 22 2006
a(41)-a(42) from Charles R Greathouse IV, Jun 05 2013

A104494 Positive integers n such that n^17 + 1 is semiprime (A001358).

Original entry on oeis.org

2, 58, 66, 166, 268, 270, 408, 600, 672, 808, 822, 970, 1050, 1090, 1150, 1200, 1212, 1380, 1578, 1752, 1912, 1950, 1986, 2016, 2038, 2292, 2340, 2548, 2590, 2656, 2718, 2800, 2856, 3162, 3300, 3342, 3738, 4138, 4152, 4228, 4270, 4272, 4362, 4782, 5080, 5166

Offset: 1

Jonathan Vos Post, Apr 19 2005

			2^17 + 1 = 131073 = 3 * 43691,
58^17 + 1 = 951208868148684143308060622849 = 59 * 16122184205909900734034925811,
66^17 + 1 = 8555529718761317069203003539457 = 67 * 127694473414348015958253784171,
1050^17 + 1 = 2292018317801032401637344360351562500000000000000001 = 1051 * 2180797638250268698037435166842590390104662226451.

Robert Price, Table of n, a(n) for n = 1..1000

Cf. A001358, A006313, A103854, A104238, A104335, A105041, A105066, A105078, A105122, A105142, A105237, A104479.

IsSemiprime:=func< n | &+[ k[2]: k in Factorization(n) ] eq 2 >; [n: n in [1..1200]|IsSemiprime(n^17+1)]; // Vincenzo Librandi, Mar 10 2015

Select[Range[1000000], PrimeQ[# + 1] && PrimeQ[(#^17 + 1)/(# + 1)] &] (* Robert Price, Mar 10 2015 *)
Select[Range[5200],PrimeOmega[#^17+1]==2&] (* Harvey P. Dale, Mar 07 2017 *)

for(n=1,3000,if(!ispseudoprime(n^17+1),forprime(p=1,10^4,if((n^17+1)%p==0,if(ispseudoprime((n^17+1)/p),print1(n,", "));break)))) \\ Derek Orr, Mar 09 2015

a(n)^17 + 1 is semiprime (A001358).

a(14)-a(46) from Robert Price, Mar 09 2015

A289182 Positions of odd semiprimes in A001358.

Original entry on oeis.org

3, 6, 7, 9, 11, 13, 15, 17, 18, 19, 20, 23, 24, 26, 28, 30, 31, 32, 34, 36, 37, 39, 40, 42, 43, 44, 46, 48, 49, 51, 53, 54, 56, 57, 59, 60, 61, 63, 65, 66, 68, 69, 71, 72, 74, 75, 77, 78, 79, 80, 81, 83, 85, 86, 89, 90, 91, 92, 94, 95, 97, 98

Offset: 1

Zak Seidov, Jun 27 2017

nonn

Complement to A115392.

Cf. A001358, A115392.

sp=Select[Range[4,1000],2==PrimeOmega[#]&];Flatten[Position[Mod[sp, 2],1]]

lista(nn) = vsp = select(x->(bigomega(x)==2), vector(nn, k, k)); select(x->(x%2), vsp, 1); \\ Michel Marcus, Jul 02 2017

from math import isqrt
from sympy import primepi, primerange
def A289182(n):
    def iterfun(f,n=0):
        m, k = n, f(n)
        while m != k: m, k = k, f(k)
        return m
    def f(x): return int(-((t:=primepi(s:=isqrt(x)))*(t-1)>>1)+sum(primepi(x//p) for p in primerange(3,s+1)))
    return f(m:=iterfun(lambda x:int(n+x-f(x)),n))+primepi(m>>1) # Chai Wah Wu, Apr 03 2025

a(n) ~ n. - Charles R Greathouse IV, Jul 02 2017

A096932 Smallest number having exactly s divisors, where s is the n-th semiprime (A001358).

Original entry on oeis.org

6, 12, 36, 48, 192, 144, 576, 3072, 1296, 12288, 9216, 196608, 5184, 786432, 36864, 12582912, 46656, 589824, 82944, 2359296, 805306368, 3221225472, 331776, 37748736, 206158430208, 746496, 3298534883328, 5308416, 13194139533312, 2415919104, 2985984, 9663676416

Offset: 1

Reinhard Zumkeller, Jul 15 2004

nonn

This is to smallest integer for which the number of divisors is the n-th prime (A061286) as semiprimes (A001358) are to primes (A000040). - Jonathan Vos Post, Feb 03 2011

Amiram Eldar, Table of n, a(n) for n = 1..1000

Cf. A000005, A001358, A005179, A061234, A061286, A061299, A084127.

s[n_] := Module[{f = FactorInteger[n], p, q}, If[Total[f[[;;,2]]] == 2, p=f[[1,1]]; q = n/p; 2^(q-1) * 3^(p-1) ,Nothing]]; Array[s, 100] (* Amiram Eldar, Apr 13 2024 *)

A000005(a(n)) = A001358(n) and A000005(m) <> A001358(n) for m < a(n).
a(n) = A005179(A001358(n)).
a(p*q) = 2^(q-1) * 3^(p-1) for primes p <= q.
a(A000040(i)*A000040(j)) = 2^(A084127(j)-1) * 3^(A084127(i)-1) for i <= j.

A104335 Positive integers n such that n^14 + 1 is semiprime (A001358).

Original entry on oeis.org

4, 74, 94, 116, 270, 464, 556, 654, 1140, 1156, 1246, 1306, 1736, 2464, 2470, 2604, 2804, 2836, 2900, 3054, 3890, 4006, 4056, 4330, 4736, 4780, 5016, 5294, 5340, 5486, 5700, 5834, 6434, 7114, 7304, 8626, 8880, 9164, 9546, 9744, 9980, 10086, 10166

Offset: 1

Jonathan Vos Post, Apr 17 2005

x^14+1 has factors (1 + x^2) (1 - x^2 + x^4 - x^6 + x^8 - x^10 + x^12).

			4^14 + 1 = 268435457 = 17 * 15790321,
74^14 + 1 = 147653612273582215982104577 = 5477 * 26958848324553992328301,
1140^14 + 1 = 6261349103849104148619671961600000000000001 = 1299601 * 4817901112610027345792802530622860401.

Robert Price, Table of n, a(n) for n = 1..1114

Cf. A001358, A085722, A096173, A186669, A104238, A103854, A105041, A105066, A105078, A105122, A105142, A105237, A104335, A104479, A104494, A104657, A105282.

Select[ Range[2, 10422, 2], PrimeQ[ #^2 + 1] && PrimeQ[ #^12 - #^10 + #^8 - #^6 + #^4 - #^2 + 1] &] (*Robert G. Wilson v, Apr 18 2005 *)
Select[Range[2,10200,2],PrimeOmega[#^14+1]==2&] (* Harvey P. Dale, Oct 16 2011 *)

More terms from Robert G. Wilson v, Apr 18 2005

A104479 Positive integers n such that n^16 + 1 is semiprime (A001358).

Original entry on oeis.org

3, 4, 9, 12, 14, 16, 18, 20, 26, 29, 40, 41, 48, 58, 70, 73, 81, 87, 92, 96, 104, 111, 113, 114, 118, 122, 130, 140, 142, 144, 146, 150, 157, 162, 164, 167, 168, 172, 173, 184, 187, 192, 194, 195, 199, 200, 202, 208, 220, 230, 232, 244, 253, 256, 266, 278, 292, 295, 298

Offset: 1

Jonathan Vos Post, Apr 18 2005

n^16 + 1 is an irreducible polynomial over Z and thus can be either prime (A006313) or semiprime.

			3^16 + 1 = 43046722 = 2 * 21523361,
4^16 + 1 = 4294967297 = 641 * 6 700417,
9^16 + 1 = 1853020188851842 = 2 * 926510094425921,
12^16 + 1 = 184884258895036417 = 153953 * 1200913648289,
200^16 + 1 = 6553600000000000000000000000000000001 =
162123499503471553 * 40423504427621041217.

Robert Price, Table of n, a(n) for n = 1..102

Cf. A006313, A001358, A085722, A096173, A186669, A104238, A103854, A105041, A105066, A105078, A105122, A105142, A105237, A104335, A104479, A104494, A104657, A105282.

IsSemiprime:=func< n | &+[ k[2]: k in Factorization(n) ] eq 2 >; [n: n in [2..300]|IsSemiprime(n^16+1)] // Vincenzo Librandi, Dec 21 2010

Select[Range[300],PrimeOmega[#^16+1]==2&] (* Harvey P. Dale, Aug 21 2011 *)
Select[Range[1000], 2 == Total[Transpose[FactorInteger[#^16 + 1]][[2]]] &] (* Robert Price, Mar 11 2015 *)

a(n)^16 + 1 is semiprime (A001358).

More terms from Vincenzo Librandi, Dec 21 2010

Corrected (adding 202, 208, and 220) by Harvey P. Dale, Aug 21 2011

A104657 Positive integers n such that n^19 + 1 is semiprime (A001358).

Original entry on oeis.org

2, 10, 28, 106, 190, 292, 556, 756, 858, 906, 1012, 1030, 1032, 1060, 1372, 1450, 1488, 1720, 1722, 1758, 1782, 1822, 1972, 2356, 2436, 2446, 2620, 2748, 2788, 2998, 3186, 3300, 3318, 3360, 3466, 3510, 3822, 3852, 4138, 4326, 4506, 4908, 5236, 5518, 5782

Offset: 1

Jonathan Vos Post, Apr 21 2005

We have the polynomial factorization: n^19 + 1 = (n + 1) * (n^18 - n^17 + n^16 - n^15 + n^14 - n^13 + n^12 - n^11 + n^10 - n^9 + n^8 - n^7 + n^6 - n^5 + n^4 - n^3 + n^2 - n + 1). Hence after the initial n=1 prime the binomial can never be prime. It can be semiprime iff n+1 is prime and (n^18 - n^17 + n^16 - n^15 + n^14 - n^13 + n^12 - n^11 + n^10 - n^9 + n^8 - n^7 + n^6 - n^5 + n^4 - n^3 + n^2 - n + 1) is prime.

			2^19 + 1 = 524289 = 3 * 174763,
10^19 + 1 = 10000000000000000001 = 11 * 909090909090909091,
1012^19 + 1 = 125438178100868833265294241234853844232270960601988910249 = 1013 * 1238284087866424810121364671617510801898035149081825373.

Robert Price, Table of n, a(n) for n = 1..1000

Cf. A001358, A006313, A103854, A104238, A104335, A105041, A105066, A105078, A105122, A105142, A105237, A104479, A104494.

IsSemiprime:=func< n | &+[ k[2]: k in Factorization(n) ] eq 2 >; [n: n in [1..1100]|IsSemiprime(n^19+1)]; // Vincenzo Librandi, Mar 10 2015

Select[Range[1000000], PrimeQ[# + 1] && PrimeQ[(#^19 + 1)/(# + 1)] &] (* Robert Price, Mar 10 2015 *)
Select[Range[5800],PrimeOmega[#^19+1]==2&] (* Harvey P. Dale, Feb 15 2019 *)

a(n)^19 + 1 is semiprime (A001358).

a(12)-a(45) from Robert Price, Mar 09 2015

cp's OEIS Frontend

A078972 Brilliant numbers: semiprimes (products of two primes, A001358) whose prime factors have the same number of decimal digits.

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A338898 Concatenated sequence of prime indices of semiprimes (A001358).

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A072000 Number of semiprimes (A001358) <= n.

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A085724 Numbers k such that 2^k - 1 is a semiprime (A001358).

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A104494 Positive integers n such that n^17 + 1 is semiprime (A001358).

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A289182 Positions of odd semiprimes in A001358.

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A096932 Smallest number having exactly s divisors, where s is the n-th semiprime (A001358).