A072931 -id:A072931 - cp's OEIS frontend

A001358 Semiprimes (or biprimes): products of two primes.

4, 6, 9, 10, 14, 15, 21, 22, 25, 26, 33, 34, 35, 38, 39, 46, 49, 51, 55, 57, 58, 62, 65, 69, 74, 77, 82, 85, 86, 87, 91, 93, 94, 95, 106, 111, 115, 118, 119, 121, 122, 123, 129, 133, 134, 141, 142, 143, 145, 146, 155, 158, 159, 161, 166, 169, 177, 178, 183, 185, 187

Offset: 1

N. J. A. Sloane, R. K. Guy

Numbers of the form p*q where p and q are primes, not necessarily distinct.
These numbers are sometimes called semiprimes or 2-almost primes.
Numbers n such that Omega(n) = 2 where Omega(n) = A001222(n) is the sum of the exponents in the prime decomposition of n.
Complement of A100959; A064911(a(n)) = 1. - Reinhard Zumkeller, Nov 22 2004
The graph of this sequence appears to be a straight line with slope 4. However, the asymptotic formula shows that the linearity is an illusion and in fact a(n)/n ~ log(n)/log(log(n)) goes to infinity. See also the graph of A066265 = number of semiprimes < 10^n.
For numbers between 33 and 15495, semiprimes are more plentiful than any other k-almost prime. See A125149.
Numbers that are divisible by exactly 2 prime powers (not including 1). - Jason Kimberley, Oct 02 2011
The (disjoint) union of A006881 and A001248. - Jason Kimberley, Nov 11 2015
An equivalent definition of this sequence is a'(n) = smallest composite number which is not divided by any smaller composite number a'(1),...,a'(n-1). - Meir-Simchah Panzer, Jun 22 2016
The above characterization can be simplified to "Composite numbers not divisible by a smaller term." This shows that this is the equivalent of primes computed via Eratosthenes's sieve, but starting with the set of composite numbers (i.e., complement of 1 union primes) instead of all positive integers > 1. It's easy to see that iterating the method (using Eratosthenes's sieve each time on the remaining numbers, complement of the previously computed set) yields numbers with bigomega = k for k = 0, 1, 2, 3, ..., i.e., {1}, A000040, this, A014612, etc. - M. F. Hasler, Apr 24 2019
For all n except n = 2, a(n) is a deficient number. - Amrit Awasthi, Sep 10 2024
It is reasonable to assume that the "comforting numbers" which John T. Williams found in Chapter 3 of Milne's book "The House at Pooh Corner" are these semiprimes. Winnie-the-Pooh wonders whether he has 14 or 15 honey pots and concludes: "It's sort of comforting." To arrange a semiprime number of honey pots in a rectangular way, let's say on a shelf, with the larger divisor parallel to the wall, there is only one solution and this is for a simple mind like Winnie-the-Pooh comforting. - Ruediger Jehn, Dec 12 2024

			From _Gus Wiseman_, May 27 2021: (Start)
The sequence of terms together with their prime factors begins:
   4 = 2*2     46 = 2*23     91 = 7*13    141 = 3*47
   6 = 2*3     49 = 7*7      93 = 3*31    142 = 2*71
   9 = 3*3     51 = 3*17     94 = 2*47    143 = 11*13
  10 = 2*5     55 = 5*11     95 = 5*19    145 = 5*29
  14 = 2*7     57 = 3*19    106 = 2*53    146 = 2*73
  15 = 3*5     58 = 2*29    111 = 3*37    155 = 5*31
  21 = 3*7     62 = 2*31    115 = 5*23    158 = 2*79
  22 = 2*11    65 = 5*13    118 = 2*59    159 = 3*53
  25 = 5*5     69 = 3*23    119 = 7*17    161 = 7*23
  26 = 2*13    74 = 2*37    121 = 11*11   166 = 2*83
  33 = 3*11    77 = 7*11    122 = 2*61    169 = 13*13
  34 = 2*17    82 = 2*41    123 = 3*41    177 = 3*59
  35 = 5*7     85 = 5*17    129 = 3*43    178 = 2*89
  38 = 2*19    86 = 2*43    133 = 7*19    183 = 3*61
  39 = 3*13    87 = 3*29    134 = 2*67    185 = 5*37
(End)

Archimedeans Problems Drive, Eureka, 17 (1954), 8.
Raymond Ayoub, An Introduction to the Analytic Theory of Numbers, Amer. Math. Soc., 1963; Chapter II, Problem 60.
Edmund Landau, Handbuch der Lehre von der Verteilung der Primzahlen, Vol. 1, Teubner, Leipzig; third edition: Chelsea, New York (1974). See p. 211.
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).
John T. Williams, Pooh and the Philosophers, Dutton Books, 1995.

N. J. A. Sloane, Table of n, a(n) for n = 1..20000 (first 10000 terms from T. D. Noe)
Dragos Crisan and Radek Erban, On the counting function of semiprimes, INTEGERS, Vol. 21 (2021), #A122.
Daniel A. Goldston, Sidney W. Graham, János Pintz and Cem Y. Yildirim, Small gaps between primes or almost primes, Transactions of the American Mathematical Society, Vol. 361, No. 10 (2009), pp. 5285-5330, arXiv preprint, arXiv:math/0506067 [math.NT], 2005.
Richard K. Guy, Letters to N. J. A. Sloane, June-August 1968
Sh. T. Ishmukhametov and F. F. Sharifullina, On distribution of semiprime numbers, Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2014, No. 8, pp. 53-59. English translation, Russian Mathematics, Vol. 58, No. 8 (2014), pp. 43-48, alternative link.
Donovan Johnson, Jonathan Vos Post, and Robert G. Wilson v, Selected n and a(n). (2.5 MB)
Dixon Jones, Quickie 593, Mathematics Magazine, Vol. 47, No. 3, May 1974, p. 167.
Edmund Landau, Handbuch der Lehre von der Verteilung der Primzahlen, vol. 1 and vol. 2, Leipzig, Berlin, B. G. Teubner, 1909. See Vol. 1, p. 211.
Xianmeng Meng, On sums of three integers with a fixed number of prime factors, Journal of Number Theory, Vol. 114, No. 1 (2005), pp. 37-65.
Michael Penn, What makes a number "good"?, YouTube video, 2022.
Carlos Rivera, Conjecture 108: On the counting function of semiprimes, The Prime Puzzles & Problems Connection.
Eric Weisstein's World of Mathematics, Semiprime.
Eric Weisstein's World of Mathematics, Almost Prime.
Wikipedia, Almost prime.
Robert G. Wilson v, Subsequences at various powers of 10.
Index to sequences related to sums of cubes
Index entries for "core" sequences

Cf. A064911 (characteristic function).
Cf. A048623, A048639, A000040 (primes), A014612 (products of 3 primes), A014613, A014614, A072000 ("pi" for semiprimes), A065516 (first differences).
Cf. A077554, A077555, A002024, A072966, A100592, A014673, A068318, A061299, A087718, A089994, A089995, A096916, A096932, A106550, A106554, A108541, A108542, A126663, A131284, A138510, A138511, A072931, A088183, A171963, A237040 (semiprimes of form n^3 + 1).
Sequences listing r-almost primes, that is, the n such that A001222(n) = r: A000040 (r=1), this sequence (r=2), A014612 (r=3), A014613 (r=4), A014614 (r=5), A046306 (r=6), A046308 (r=7), A046310 (r=8), A046312 (r=9), A046314 (r=10), A069272 (r=11), A069273 (r=12), A069274 (r=13), A069275 (r=14), A069276 (r=15), A069277 (r=16), A069278 (r=17), A069279 (r=18), A069280 (r=19), A069281 (r=20).
These are the Heinz numbers of length-2 partitions, counted by A004526.
The squarefree case is A006881 with odd/even terms A046388/A100484 (except 4).
Including primes gives A037143.
The odd/even terms are A046315/A100484.
Partial sums are A062198.
The prime factors are A084126/A084127.
Grouping by greater factor gives A087112.
The product/sum/difference of prime indices is A087794/A176504/A176506.
Positions of even/odd terms are A115392/A289182.
The terms with relatively prime/divisible prime indices are A300912/A318990.
Factorizations using these terms are counted by A320655.
The prime indices are A338898/A338912/A338913.
Grouping by weight (sum of prime indices) gives A338904, with row sums A024697.
The terms with even/odd weight are A338906/A338907.
The terms with odd/even prime indices are A338910/A338911.
The least/greatest term of weight n is A339114/A339115.
Cf. A014342, A098350, A112141, A320732, A332765, A339003/A339004, A339116.

a001358 n = a001358_list !! (n-1)
a001358_list = filter ((== 2) . a001222) [1..]

[n: n in [2..200] | &+[d[2]: d in Factorization(n)] eq 2]; // Bruno Berselli, Sep 09 2015

A001358 := proc(n) option remember; local a; if n = 1 then 4; else for a from procname(n-1)+1 do if numtheory[bigomega](a) = 2 then return a; end if; end do: end if; end proc:
seq(A001358(n), n=1..120) ; # R. J. Mathar, Aug 12 2010

Select[Range[200], Plus@@Last/@FactorInteger[#] == 2 &] (* Zak Seidov, Jun 14 2005 *)
Select[Range[200], PrimeOmega[#]==2&] (* Harvey P. Dale, Jul 17 2011 *)

select( isA001358(n)={bigomega(n)==2}, [1..199]) \\ M. F. Hasler, Apr 09 2008; added select() Apr 24 2019

list(lim)=my(v=List(),t);forprime(p=2, sqrt(lim), t=p;forprime(q=p, lim\t, listput(v,t*q))); vecsort(Vec(v)) \\ Charles R Greathouse IV, Sep 11 2011

A1358=List(4); A001358(n)={while(#A1358M. F. Hasler, Apr 24 2019

from sympy import factorint
def ok(n): return sum(factorint(n).values()) == 2
print([k for k in range(1, 190) if ok(k)]) # Michael S. Branicky, Apr 30 2022

from math import isqrt
from sympy import primepi, prime
def A001358(n):
    def f(x): return int(n+x-sum(primepi(x//prime(k))-k+1 for k in range(1, primepi(isqrt(x))+1)))
    m, k = n, f(n)
    while m != k:
        m, k = k, f(k)
    return m # Chai Wah Wu, Jul 23 2024

a(n) ~ n*log(n)/log(log(n)) as n -> infinity [Landau, p. 211], [Ayoub].
Recurrence: a(1) = 4; for n > 1, a(n) = smallest composite number which is not a multiple of any of the previous terms. - Amarnath Murthy, Nov 10 2002
A174956(a(n)) = n. - Reinhard Zumkeller, Apr 03 2010
a(n) = A088707(n) - 1. - Reinhard Zumkeller, Feb 20 2012
Sum_{n>=1} 1/a(n)^s = (1/2)*(P(s)^2 + P(2*s)), where P is the prime zeta function. - Enrique Pérez Herrero, Jun 24 2012
sigma(a(n)) + phi(a(n)) - mu(a(n)) = 2*a(n) + 1. mu(a(n)) = ceiling(sqrt(a(n))) - floor(sqrt(a(n))). - Wesley Ivan Hurt, May 21 2013
mu(a(n)) = -Omega(a(n)) + omega(a(n)) + 1, where mu is the Moebius function (A008683), Omega is the count of prime factors with repetition, and omega is the count of distinct prime factors. - Alonso del Arte, May 09 2014
a(n) = A078840(2,n). - R. J. Mathar, Jan 30 2019
A100484 UNION A046315. - R. J. Mathar, Apr 19 2023
Conjecture: a(n)/n ~ (log(n)/log(log(n)))*(1-(M/log(log(n)))) as n -> oo, where M is the Mertens's constant (A077761). - Alain Rocchelli, Feb 02 2025

More terms from James Sellers, Aug 22 2000

A344447 Number T(n,k) of partitions of n into k semiprimes; triangle T(n,k), n>=0, read by rows.

Original entry on oeis.org

1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 2, 2, 1, 0, 0, 2, 1, 0, 0, 2, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 3, 2, 1, 0, 0, 1, 2, 1, 0, 0, 2, 3, 2, 1, 1, 0, 1, 2, 2, 1, 1, 0, 1, 1, 2, 3, 2, 1, 0, 0, 1, 3, 3, 1, 0, 0, 2, 3, 4, 2, 1, 1

Offset: 0

Alois P. Heinz, May 19 2021

T(n,k) is defined for all n,k >= 0. The triangle contains in each row n only the terms for k=0 and then up to the last positive T(n,k) (if it exists).

			Triangle T(n,k) begins:
  1 ;
  0 ;
  0 ;
  0 ;
  0, 1 ;
  0    ;
  0, 1 ;
  0    ;
  0, 0, 1 ;
  0, 1    ;
  0, 1, 1 ;
  0       ;
  0, 0, 1, 1 ;
  0, 0, 1    ;
  0, 1, 1, 1 ;
  0, 1, 1    ;
  0, 0, 1, 1, 1 ;
  0, 0, 0, 1    ;
  0, 0, 2, 2, 1 ;
  0, 0, 2, 1    ;
  0, 0, 2, 1, 1, 1 ;
  ...

Alois P. Heinz, Rows n = 0..500, flattened

Columns k=0-10 give: A000007, A064911, A072931, A344446, A340756, A344245, A344246, A344254, A344255, A344256, A344257.
Row sums give A101048.
T(4n,n) gives A000012.
Cf. A001358, A117278, A281617.

h:= proc(n) option remember; `if`(n=0, 0,
     `if`(numtheory[bigomega](n)=2, n, h(n-1)))
    end:
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
     `if`(i>n, 0, expand(x*b(n-i, h(min(n-i, i)))))+b(n, h(i-1))))
    end:
T:= n-> (p-> seq(coeff(p, x, i), i=0..max(0, degree(p))))(b(n, h(n))):
seq(T(n), n=0..32);

h[n_] := h[n] = If[n == 0, 0,
     If[PrimeOmega[n] == 2, n, h[n-1]]];
b[n_, i_] := b[n, i] = If[n == 0, 1, If[i < 1, 0,
     If[i > n, 0, Expand[x*b[n-i, h[Min[n-i, i]]]]] + b[n, h[i-1]]]];
T[n_] := Table[Coefficient[#, x, i], {i, 0, Max[0, Exponent[#, x]]}]&[b[n, h[n]]];
Table[T[n], {n, 0, 32}] // Flatten (* Jean-François Alcover, Aug 19 2021, after Alois P. Heinz *)

T(n,k) = [x^n y^k] 1/Product_{j>=1} (1-y*x^A001358(j)).

Sum_{k>0} k * T(n,k) = A281617(n).

A072966 Numbers which are not the sum of two semiprimes.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 9, 11, 17, 22, 33

Offset: 1

Lior Manor, Aug 13 2002

nonn

Is this sequence finite?

See the graph of sequence A072931 for compelling evidence that 33 is the last term of this sequence. - T. D. Noe, Apr 11 2007

			a(10) = 11 since there is no way to represent 11 as a sum of two semiprimes. 13 is not a term since 13 = 4 + 9.

Cf. A001358.

lim = 10000;
s = Select[Range[lim], PrimeOmega[#] == 2 &];
c = Map[Total,Union[Subsets[s, {2}], Table[{s[[i]], s[[i]]}, {i, 1, Length[s]}]]];
Join[Complement[Range[0, lim], c], ">", lim ](* Robert Price, Mar 30 2019 *)

A088183 Number of ways to write n as a sum of two coprime semiprimes.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 3, 0, 0, 1, 1, 0, 2, 0, 2, 0, 2, 0, 4, 1, 0, 1, 4, 0, 2, 0, 1, 0, 3, 0, 4, 0, 1, 2, 5, 0, 6, 0, 1, 3, 1, 0, 4, 1, 3, 0, 6, 0, 5, 3, 1, 2, 3, 0, 5, 0, 3, 2, 7, 0, 1, 3, 4, 1, 4, 0, 6, 2, 2, 3, 6, 0, 7, 1, 4, 2, 6, 1

Offset: 1

Reinhard Zumkeller, Sep 22 2003

nonn

a(A088184(n))>0, a(A088185(n))=0.
Is a(n)>0 for n>210? see conjecture in A072931.
The graph of this sequence is compelling evidence that 210 is the last term of sequence A088185. - T. D. Noe, Apr 10 2007

			a(64)=3: 64 = 3*3+5*11 = 3*5+7*7 = 5*5+3*13, (A072931(64)=5).

T. D. Noe, Table of n, a(n) for n=1..10000
Eric Weisstein's World of Mathematics, Semiprime
Eric Weisstein's World of Mathematics, Relatively Prime

Cf. A072931, A001358.

cpspQ[{a_,b_}]:=PrimeOmega[a]==PrimeOmega[b]==2&&CoprimeQ[a,b]; Table[ Count[ IntegerPartitions[n,{2}],?(cpspQ[#]&)],{n,110}] (* _Harvey P. Dale, Sep 10 2019 *)

a(n)=sum(i=1, n, sum(j=1, i, if (gcd(i,j)==1, if (abs(bigomega(i)-2) +abs(bigomega(j)-2) +abs(n-i-j),0,1)))) \\ after A072966; Michel Marcus, Sep 08 2015

A100592 Least positive integer that can be represented as the sum of exactly two semiprimes in exactly n ways.

Original entry on oeis.org

1, 8, 18, 30, 43, 48, 60, 72, 91, 108, 132, 155, 120, 144, 192, 168, 216, 236, 227, 180, 320, 340, 240, 252, 348, 300, 324, 336, 488, 484, 456, 396, 614, 360, 524, 548, 706, 468, 536, 656, 628, 420, 624, 576, 612, 588, 540, 600, 648, 768, 732, 800, 832, 660

Offset: 0

Jonathan Vos Post, Nov 30 2004

A072931(a(n)) = n and A072931(m) < n for m < a(n). [From Reinhard Zumkeller, Jan 21 2010]

			a(0) = 1 because 1 is the smallest positive integer that cannot be represented as sum of two semiprimes (since 4 is the smallest semiprime). a(1) = 8 because 8 is the smallest such sum of two semiprimes: 4 + 4. Similarly a(2) = 18 because 18 = 14 + 4 = 9 + 9 where {4,9,14} are semiprimes and there is no third such sum for 18.

Reinhard Zumkeller and Zak Seidov, Table of n, a(n) for n = 0..1000 (Terms 0-250 from Reinhard Zumkeller)

Cf. A001358, A076768, A100570, A072966.

a(n) = min{i such that i = A001358(j) + A001358(k) in n ways}.

A171963 Number of partitions of the n-th semiprime into two semiprimes.

Original entry on oeis.org

0, 0, 0, 1, 1, 1, 1, 0, 2, 1, 0, 1, 3, 1, 3, 1, 3, 1, 5, 2, 2, 1, 3, 3, 3, 4, 2, 2, 4, 4, 8, 3, 3, 8, 4, 5, 8, 3, 6, 7, 3, 5, 7, 9, 5, 5, 7, 10, 7, 6, 11, 5, 8, 7, 5, 9, 8, 8, 9, 6, 10, 8, 8, 7, 11, 9, 9, 10, 9, 7, 15, 12, 10, 11, 9, 10, 15, 9, 12, 10, 12, 12, 13, 11, 11, 11, 15, 12, 17, 12, 13, 16, 14

Offset: 1

Reinhard Zumkeller, Jan 21 2010

nonn

a(n) = A072931(A001358(n)).

			a(13) = A072931(A001358(13)) = A072931(35) = #{26+9,25+10,21+14} = #{2*13+3*3,5*5+2*5,3*7+2*7} = 3.

R. Zumkeller, Table of n, a(n) for n = 1..1000

A172366 Number of partitions of prime(n) into the sum of two semiprimes.

Original entry on oeis.org

0, 0, 0, 0, 0, 1, 0, 2, 1, 2, 3, 2, 2, 4, 4, 3, 5, 6, 4, 6, 5, 5, 7, 4, 7, 6, 7, 7, 5, 5, 8, 8, 8, 8, 9, 10, 9, 7, 13, 10, 10, 11, 13, 10, 10, 10, 11, 15, 18, 13, 10, 13, 14, 16, 12, 18, 12, 15, 12, 11

Offset: 1

Juri-Stepan Gerasimov, Nov 20 2010

nonn

			a(8)=2 because prime(8)=19=4(semiprime)+15(semiprime)=9(semiprime)+10(semiprime).

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A129363, A175933,

Table[Total[If[PrimeOmega[#]=={2,2},1,0]&/@Table[{x-n,n},{n,x/2}]],{x, Prime[ Range[60]]}] (* Harvey P. Dale, Dec 21 2015 *)

a(n) = A072931(A000040(n)).

Corrected and extended by D. S. McNeil, Nov 20 2010

A302301 Number of ways to write n as a sum of two distinct semiprimes.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 2, 1, 1, 0, 1, 2, 2, 1, 1, 1, 2, 2, 3, 2, 0, 1, 3, 3, 2, 1, 3, 3, 2, 2, 4, 3, 2, 1, 4, 5, 3, 2, 1, 2, 3, 2, 5, 3, 2, 2, 5, 6, 6, 1, 3, 5, 3, 3, 4, 4, 3, 2, 6, 7, 5, 3, 3, 3, 4, 3, 5, 5, 3, 2, 7, 7, 2, 4

Offset: 0

Wesley Ivan Hurt, Apr 04 2018

			a(19) = 2; 19 = 15+4 = 10+9.

Alois P. Heinz, Table of n, a(n) for n = 0..20000 (first 1000 terms from Harvey P. Dale)
Index entries for sequences related to partitions

Cf. A001222, A001358, A072931.

h:= proc(n) option remember; `if`(n=0, 0,
     `if`(numtheory[bigomega](n)=2, n, h(n-1)))
    end:
b:= proc(n, i) option remember; series(`if`(n=0, 1, `if`(i<1, 0,
     `if`(i>n, 0, x*b(n-i, h(min(n-i, i-1))))+b(n, h(i-1)))), x, 3)
    end:
a:= n-> coeff(b(n, h(n)), x, 2):
seq(a(n), n=0..120);  # Alois P. Heinz, May 26 2021

Table[Sum[KroneckerDelta[PrimeOmega[i], 2] KroneckerDelta[PrimeOmega[n - i], 2], {i, Floor[(n - 1)/2]}], {n, 100}]
Table[Count[IntegerPartitions[n,{2}],?(PrimeOmega[#[[1]]]==PrimeOmega[#[[2]]]==2&&#[[1]]!=#[[2]]&)],{n,90}] (* _Harvey P. Dale, Aug 03 2020 *)

a(n) = sum(i=1, (n-1)\2, (bigomega(i)==2)*(bigomega(n-i)==2)); \\ Michel Marcus, Apr 08 2018

a(n) = Sum_{i=1..floor((n-1)/2)} [Omega(i) = 2] * [Omega(n-i) = 2], where Omega = A001222 and [] is the Iverson bracket.

A329481 Numbers which are not the sum of two squarefree semiprimes.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 17, 18, 19, 22, 23, 26, 33, 34, 38, 46, 51, 58, 62, 82

Offset: 1

Lior Manor, Nov 14 2019

nonn

Is this a finite sequence?

Most probably yes. Since almost all semiprimes are squarefree, this is essentially the same as A072966. The graph of A072931 would not change qualitatively if only squarefree semiprimes were considered. - M. F. Hasler, Dec 03 2019

			a(10) = 11 since there is no way to represent 11 as a sum of two squarefree semiprimes. 12 is not a term since 12 = 6 + 6.

Cf. A006881, A072966.

cp's OEIS Frontend

A001358 Semiprimes (or biprimes): products of two primes.

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A344447 Number T(n,k) of partitions of n into k semiprimes; triangle T(n,k), n>=0, read by rows.

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A072966 Numbers which are not the sum of two semiprimes.

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A088183 Number of ways to write n as a sum of two coprime semiprimes.

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A100592 Least positive integer that can be represented as the sum of exactly two semiprimes in exactly n ways.

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A171963 Number of partitions of the n-th semiprime into two semiprimes.

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A172366 Number of partitions of prime(n) into the sum of two semiprimes.

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