A089995 -id:A089995 - cp's OEIS frontend

A175586 Duplicate of A089995.

10, 14, 21, 22, 26, 33, 34, 38, 39, 46, 51, 55, 57, 58, 62, 65, 69, 74, 82, 85, 86, 87, 91, 93, 94, 95, 106, 111, 115, 118, 119, 122, 123, 129, 133, 134, 141, 142, 145

Offset: 1

dead

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

Original entry on oeis.org

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

A084127 Prime factor >= other prime factor of n-th semiprime.

Original entry on oeis.org

2, 3, 3, 5, 7, 5, 7, 11, 5, 13, 11, 17, 7, 19, 13, 23, 7, 17, 11, 19, 29, 31, 13, 23, 37, 11, 41, 17, 43, 29, 13, 31, 47, 19, 53, 37, 23, 59, 17, 11, 61, 41, 43, 19, 67, 47, 71, 13, 29, 73, 31, 79, 53, 23, 83, 13, 59, 89, 61, 37, 17, 97, 67, 101, 29, 41, 103, 19, 71, 107, 43, 31

Offset: 1

Reinhard Zumkeller, May 15 2003

nonn

Largest nontrivial divisor of n-th semiprime. [Juri-Stepan Gerasimov, Apr 18 2010]

Greater of the prime factors of A001358(n). - Jianing Song, Aug 05 2022

Zak Seidov, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, Semiprime

Cf. A001358 (the semiprimes), A084126 (lesser of the prime factors of the semiprimes).

Cf. A014673, A061299, A068318, A087718, A087794, A089994, A089995, A096932, A106550, A106554, A108542, A126663, A131284, A138510, A138511.

a084127 = a006530 . a001358  -- Reinhard Zumkeller, Nov 25 2012

FactorInteger[#][[-1, 1]]& /@ Select[Range[1000], PrimeOmega[#] == 2&] (* Jean-François Alcover, Nov 17 2021 *)

lista(nn) = {for (n=2, nn, if (bigomega(n)==2, f = factor(n); print1(f[length(f~),1], ", ")););} \\ Michel Marcus, Jun 05 2013

from math import isqrt
from sympy import primepi, primerange, primefactors
def A084127(n):
    def bisection(f,kmin=0,kmax=1):
        while f(kmax) > kmax: kmax <<= 1
        while kmax-kmin > 1:
            kmid = kmax+kmin>>1
            if f(kmid) <= kmid:
                kmax = kmid
            else:
                kmin = kmid
        return kmax
    def f(x): return int(n+x+((t:=primepi(s:=isqrt(x)))*(t-1)>>1)-sum(primepi(x//p) for p in primerange(s+1)))
    return max(primefactors(bisection(f,n,n))) # Chai Wah Wu, Oct 23 2024

a(n) = A006530(A001358(n)).
a(n) = A001358(n)/A020639(A001358(n)). [corrected by Michel Marcus, Jul 18 2020]
a(n) = A001358(n)/A084126(n).

Corrected by T. D. Noe, Nov 15 2006

A084126 Prime factor <= other prime factor of n-th semiprime.

Original entry on oeis.org

2, 2, 3, 2, 2, 3, 3, 2, 5, 2, 3, 2, 5, 2, 3, 2, 7, 3, 5, 3, 2, 2, 5, 3, 2, 7, 2, 5, 2, 3, 7, 3, 2, 5, 2, 3, 5, 2, 7, 11, 2, 3, 3, 7, 2, 3, 2, 11, 5, 2, 5, 2, 3, 7, 2, 13, 3, 2, 3, 5, 11, 2, 3, 2, 7, 5, 2, 11, 3, 2, 5, 7, 2, 3, 13, 2, 5, 3, 13, 3, 11, 2, 7, 2, 5, 3, 2, 2, 7, 17, 3, 5, 2, 13, 7, 2, 3, 5, 3, 2

Offset: 1

Reinhard Zumkeller, May 15 2003

nonn

Lesser of the prime factors of A001358(n). - Jianing Song, Aug 05 2022

Zak Seidov, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, Semiprime

Cf. A001358 (the semiprimes), A084127 (greater of the prime factors of the semiprimes).

Cf. A068318, A087718, A087794, A089994, A089995, A096916, A106550, A106554, A108541, A131284, A138510, A138511.

a084126 = a020639 . a001358  -- Reinhard Zumkeller, Nov 25 2012

FactorInteger[#][[1,1]]&/@Select[Range[500],PrimeOmega[#]==2&] (* Harvey P. Dale, Jun 25 2018 *)

from sympy import primepi, primerange, primefactors
def A084126(n):
    def bisection(f,kmin=0,kmax=1):
        while f(kmax) > kmax: kmax <<= 1
        kmin = kmax >> 1
        while kmax-kmin > 1:
            kmid = kmax+kmin>>1
            if f(kmid) <= kmid:
                kmax = kmid
            else:
                kmin = kmid
        return kmax
    def f(x): return int(n+x+((t:=primepi(s:=isqrt(x)))*(t-1)>>1)-sum(primepi(x//p) for p in primerange(s+1)))
    return min(primefactors(bisection(f,n,n))) # Chai Wah Wu, Apr 03 2025

a(n) = A020639(A001358(n)).
a(n) = A001358(n)/A006530(A001358(n)). [corrected by Michel Marcus, Jul 18 2020]
a(n) = A001358(n)/A084127(n).

A325160 Products of distinct, non-consecutive primes. Squarefree numbers not divisible by any two consecutive primes.

Original entry on oeis.org

1, 2, 3, 5, 7, 10, 11, 13, 14, 17, 19, 21, 22, 23, 26, 29, 31, 33, 34, 37, 38, 39, 41, 43, 46, 47, 51, 53, 55, 57, 58, 59, 61, 62, 65, 67, 69, 71, 73, 74, 79, 82, 83, 85, 86, 87, 89, 91, 93, 94, 95, 97, 101, 103, 106, 107, 109, 110, 111, 113, 115, 118, 119

Offset: 1

Gus Wiseman, Apr 05 2019

nonn

The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k), so these are Heinz numbers of integer partitions into distinct non-consecutive parts (counted by A003114). The nonsquarefree case is A319630, which gives the Heinz numbers of integer partitions with no consecutive parts (counted by A116931).

The numbers of terms not exceeding 10^k, for k = 1, 2, ..., are 6, 52, 515, 5146, 51435, 514416, 5144232, 51442384, ... . Apparently, the asymptotic density of this sequence exists and equals 0.51442... . - Amiram Eldar, Sep 24 2022

			The sequence of terms together with their prime indices begins:
   1: {}
   2: {1}
   3: {2}
   5: {3}
   7: {4}
  10: {1,3}
  11: {5}
  13: {6}
  14: {1,4}
  17: {7}
  19: {8}
  21: {2,4}
  22: {1,5}
  23: {9}
  26: {1,6}
  29: {10}
  31: {11}
  33: {2,5}
  34: {1,7}
  37: {12}

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A001227, A003114, A005117, A025157, A034296, A056239, A073485, A073491, A089995, A112798, A116931, A319630, A325161, A325162.

Select[Range[100],Min@@Differences[Flatten[Cases[FactorInteger[#],{p_,k_}:>Table[PrimePi[p],{k}]]]]>1&]

isok(k) = {if (issquarefree(k), my(v = apply(primepi, factor(k)[,1])); ! #select(x->(v[x+1]-v[x] == 1), [1..#v-1]));} \\ Michel Marcus, Jan 09 2021

A325161 Nonprime squarefree numbers not divisible by any two consecutive primes.

Original entry on oeis.org

1, 10, 14, 21, 22, 26, 33, 34, 38, 39, 46, 51, 55, 57, 58, 62, 65, 69, 74, 82, 85, 86, 87, 91, 93, 94, 95, 106, 110, 111, 115, 118, 119, 122, 123, 129, 130, 133, 134, 141, 142, 145, 146, 155, 158, 159, 161, 166, 170, 177, 178, 182, 183, 185, 187, 190, 194, 201

Offset: 1

Gus Wiseman, Apr 05 2019

nonn

The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k), so these are Heinz numbers of non-singleton integer partitions into distinct non-consecutive parts (counted by A003114 minus 1).

			The sequence of terms together with their prime indices begins:
   1: {}
  10: {1,3}
  14: {1,4}
  21: {2,4}
  22: {1,5}
  26: {1,6}
  33: {2,5}
  34: {1,7}
  38: {1,8}
  39: {2,6}
  46: {1,9}
  51: {2,7}
  55: {3,5}
  57: {2,8}
  58: {1,10}
  62: {1,11}
  65: {3,6}
  69: {2,9}
  74: {1,12}
  82: {1,13}

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A001227, A003114, A005117, A025157, A034296, A056239, A073485, A073491, A089995, A112798, A116931, A319630, A325160, A325162.

Select[Range[100],!PrimeQ[#]&&Min@@Differences[Flatten[Cases[FactorInteger[#],{p_,k_}:>Table[PrimePi[p],{k}]]]]>1&]

A089994 Number of primes between factors of n-th semiprime.

Original entry on oeis.org

0, 0, 0, 1, 2, 0, 1, 3, 0, 4, 2, 5, 0, 6, 3, 7, 0, 4, 1, 5, 8, 9, 2, 6, 10, 0, 11, 3, 12, 7, 1, 8, 13, 4, 14, 9, 5, 15, 2, 0, 16, 10, 11, 3, 17, 12, 18, 0, 6, 19, 7, 20, 13, 4, 21, 0, 14, 22, 15, 8, 1, 23, 16, 24, 5, 9, 25, 2, 17, 26, 10, 6, 27, 18, 0, 28, 11, 19, 1, 20, 3, 29, 7, 30

Offset: 1

Reinhard Zumkeller, Nov 19 2003

nonn

a(m)=0 iff m in A033476; a(m)>0 iff m in A089995.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A001358, A033476, A089995, A084126, A084127, A000720.

pbfs[n_]:=Module[{f=PrimePi/@Transpose[FactorInteger[n]][[1]]}, Max[ 0,Last[f]-First[f]-1]]; pbfs/@Select[Range[300],PrimeOmega[#]==2&] (* Harvey P. Dale, Apr 09 2012 *)

A325162 Squarefree numbers with no two prime indices differing by less than 3.

Original entry on oeis.org

1, 2, 3, 5, 7, 11, 13, 14, 17, 19, 22, 23, 26, 29, 31, 33, 34, 37, 38, 39, 41, 43, 46, 47, 51, 53, 57, 58, 59, 61, 62, 65, 67, 69, 71, 73, 74, 79, 82, 83, 85, 86, 87, 89, 93, 94, 95, 97, 101, 103, 106, 107, 109, 111, 113, 115, 118, 119, 122, 123, 127, 129, 131

Offset: 1

Gus Wiseman, Apr 05 2019

nonn

A prime index of n is a number m such that prime(m) divides n.

The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k), so these are Heinz numbers of integer partitions into distinct parts, no two differing by less than 3 (counted by A025157).

			The sequence of terms together with their prime indices begins:
   1: {}
   2: {1}
   3: {2}
   5: {3}
   7: {4}
  11: {5}
  13: {6}
  14: {1,4}
  17: {7}
  19: {8}
  22: {1,5}
  23: {9}
  26: {1,6}
  29: {10}
  31: {11}
  33: {2,5}
  34: {1,7}
  37: {12}
  38: {1,8}
  39: {2,6}

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A001227, A003114, A005117, A025157, A034296, A056239, A073485, A073491, A089995, A112798, A116931, A319630, A325160, A325161.

filter:= proc(n) local F;
  F:= ifactors(n)[2];
  if ormap(t -> t[2]>1, F) then return false fi;
  if nops(F) <= 1 then return true fi;
  F:= map(numtheory:-pi,sort(map(t -> t[1],F)));
  min(F[2..-1]-F[1..-2]) >= 3;
end proc:
select(filter, [$1..200]); # Robert Israel, Apr 08 2019

Select[Range[100],Min@@Differences[Flatten[Cases[FactorInteger[#],{p_,k_}:>Table[PrimePi[p],{k}]]]]>2&]

cp's OEIS Frontend

A175586 Duplicate of A089995.

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

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A084127 Prime factor >= other prime factor of n-th semiprime.

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A084126 Prime factor <= other prime factor of n-th semiprime.

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A325160 Products of distinct, non-consecutive primes. Squarefree numbers not divisible by any two consecutive primes.

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A325161 Nonprime squarefree numbers not divisible by any two consecutive primes.

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A089994 Number of primes between factors of n-th semiprime.

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