A124270 -id:A124270 - cp's OEIS frontend

A124268 Primes indexed by 3-almost primes.

19, 37, 61, 71, 103, 107, 113, 181, 193, 197, 229, 239, 307, 317, 337, 349, 379, 383, 397, 479, 521, 523, 557, 571, 601, 619, 641, 643, 683, 691, 733, 787, 853, 857, 883, 887, 971, 977, 1013, 1019, 1021, 1033, 1039, 1091, 1109, 1123, 1151, 1187, 1279

Offset: 1

Jonathan Vos Post, Oct 23 2006

3-almost primes indexed by primes = A124269. prime(3almostprime(n)) - 3almostprime(prime(n)) = A124270. See also A106349 Primes indexed by semiprimes. See also A106350 Semiprimes indexed by primes. See also A122824 Prime(semiprime(n)) - semiprime(prime(n)). Commutator [A000040,A001358] at n.

			a(1) = prime(3almostprime(1)) = prime(8) = 19.
a(2) = prime(3almostprime(2)) = prime(12) = 37.
a(3) = prime(3almostprime(3)) = prime(18) = 61.

Giovanni Resta, Table of n, a(n) for n = 1..10000

Cf. A000040, A014612, A122824, A124269, A124270.

Prime[#]&/@Select[Range[400],PrimeOmega[#]==3&] (* Harvey P. Dale, Mar 19 2020 *)

a(n) = prime(3almostprime(n)) = A000040(A014612(n)). {p such that p is prime and omega(primepi(p)) = 3} = {p such that p is in A000040 and A001222(A000720(p)) = 3}.

A124269 3-almost primes indexed by primes.

Original entry on oeis.org

12, 18, 27, 30, 50, 63, 75, 78, 102, 124, 130, 164, 172, 175, 190, 231, 246, 258, 279, 286, 292, 332, 345, 369, 404, 418, 425, 430, 435, 452, 524, 539, 574, 578, 606, 610, 638, 652, 663, 692, 722, 725, 775, 782, 795, 801, 854, 906, 916, 927, 938, 963, 969

Offset: 1

Jonathan Vos Post, Oct 23 2006

Primes indexed by 3-almostprimes = A124268. prime(3almostprime(n)) - 3almostprime(prime(n)) = A124270. See also A106349 Primes indexed by semiprimes. See also A106350 Semiprimes indexed by primes. See also A122824 Prime(semiprime(n)) - semiprime(prime(n)). Commutator [A000040,A001358] at n.

			a(1) = 3almostprime(prime(1)) = 3almostprime(2) = 12 = 2^2 * 3.
a(2) = 3almostprime(prime(2)) = 3almostprime(3) = 18 = 2 * 3^2.
a(3) = 3almostprime(prime(3)) = 3almostprime(5) = 27 = 3^3.

Giovanni Resta, Table of n, a(n) for n = 1..10000

Cf. A000040, A014612, A122824, A124268, A124270.

From R. J. Mathar, Oct 15 2010: (Start)
A014612 := proc(n) option remember; if n = 1 then 8; else for a from procname(n-1)+1 do if numtheory[bigomega](a) = 3 then return a; end if; end do; end if; end proc:
A124269 := proc(n) A014612(ithprime(n)) ; end proc: seq(A124269(n),n=1..80) ; (End)

p3 = Select[Range[1000], PrimeOmega[#] == 3 &]; p3[[Prime@ Range@ PrimePi@ Length@ p3]] (* Giovanni Resta, Jun 13 2016 *)

a(n) = 3almostprime(prime(n)) = A014612(A000040(n)).

More terms from R. J. Mathar, Oct 15 2010

A124282 Primes indexed by 4-almost primes.

Original entry on oeis.org

53, 89, 151, 173, 251, 263, 281, 419, 433, 457, 463, 541, 569, 701, 743, 761, 769, 809, 863, 881, 911, 1097, 1129, 1193, 1213, 1249, 1291, 1373, 1427, 1439, 1459, 1481, 1571, 1583, 1657, 1783, 1931, 1949, 1951, 2017, 2029, 2087, 2203, 2213, 2287, 2297

Offset: 1

Jonathan Vos Post, Oct 24 2006

4-almost primes indexed by primes = A124283. prime(4almostprime(n)) - 4almostprime(prime(n)) = A124284. Primes indexed by 3-almost primes = A124268. 3-almost primes indexed by primes = A124269. prime(3almostprime(n)) - 3almostprime(prime(n)) = A124270. See also A106349 Primes indexed by semiprimes. See also A106350 Semiprimes indexed by primes. See also A122824 Prime(semiprime(n)) - semiprime(prime(n)). Commutator [A000040,A001358] at n.

			a(1) = prime(4almostprime(1)) = prime(16) = 53.
a(2) = prime(4almostprime(2)) = prime(24) = 89.
a(3) = prime(4almostprime(3)) = prime(36) = 151.

Giovanni Resta, Table of n, a(n) for n = 1..10000

Cf. A000040, A014613, A114414, A122824, A124269, A124270, A124283, A124284.

a(n) = prime(4almostprime(n)) = A000040(A014613(n)). {p such that p is prime and omega(primepi(p)) = 4} = {p such that p is in A000040 and A001222(A000720(p)) = 4}.

A124283 4-almost primes indexed by primes.

Original entry on oeis.org

24, 36, 54, 60, 90, 104, 136, 150, 189, 225, 232, 294, 308, 328, 344, 375, 441, 459, 488, 510, 516, 550, 570, 621, 676, 708, 714, 738, 748, 776, 852, 860, 884, 910, 999, 1014, 1060, 1096, 1112, 1161, 1197, 1206, 1256, 1274, 1284, 1290, 1356, 1432, 1450, 1482

Offset: 1

Jonathan Vos Post, Oct 24 2006

Primes indexed by 4-almost primes = A124282. prime(4almostprime(n)) - 4almostprime(prime(n)) = A124284. Primes indexed by 3-almost primes = A124268. 3-almost primes indexed by primes = A124269. prime(3almostprime(n)) - 3almostprime(prime(n)) = A124270. See also A106349 Primes indexed by semiprimes. See also A106350 Semiprimes indexed by primes. See also A122824 Prime(semiprime(n)) - semiprime(prime(n)). Commutator [A000040,A001358] at n.

			a(1) = 4almostprime(prime(1)) = 4almostprime(2) = 24.
a(2) = 4almostprime(prime(2)) = 4almostprime(3) = 36.
a(3) = 4almostprime(prime(3)) = 4almostprime(5) = 54.

Giovanni Resta, Table of n, a(n) for n = 1..10000

Cf. A000040, A014613, A114414, A122824, A124269, A124270, A124282, A124284.

from math import isqrt
from sympy import prime, primepi, integer_nthroot, primerange
def A124283(n):
    def f(x): return int(prime(n)+x-sum(primepi(x//(k*m*r))-c for a, k in enumerate(primerange(integer_nthroot(x, 4)[0]+1)) for b, m in enumerate(primerange(k, integer_nthroot(x//k, 3)[0]+1), a) for c, r in enumerate(primerange(m, isqrt(x//(k*m))+1), b)))
    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
    return bisection(f,n,n) # Chai Wah Wu, Sep 09 2024

a(n) = 4almostprime(prime(n)) = A014613(A000040(n)).

a(17)-a(50) from Giovanni Resta, Jun 13 2016

A124284 Prime(4almostprime(n))-4almostprime(prime(n)). Commutator [A000040,A014613] at n.

Original entry on oeis.org

29, 53, 97, 113, 161, 159, 145, 269, 244, 232, 231, 247, 261, 373, 399, 386, 328, 350, 375, 371, 395, 547, 559, 572, 537, 541, 577, 635, 679, 663, 607, 621, 687, 673, 658, 769, 871, 853, 839, 856, 832, 881, 947, 939, 1003, 1007, 955, 915, 907, 889, 941, 989

Offset: 1

Jonathan Vos Post, Oct 24 2006

			a(1) = prime(4almostprime(1)) - 4almostprime(prime(1)) = 53 - 24 = 29.
a(2) = prime(4almostprime(2)) - 4almostprime(prime(2)) = 89 - 36 = 53.
a(3) = prime(4almostprime(3)) - 4almostprime(prime(3)) = 151 - 54 = 97.
It is mere coincidence that the first 4 values are all primes.

Robert G. Wilson v, Table of n, a(n) for n=1..1000

Cf. Primes indexed by 4-almost primes = A124282. 4-almost primes indexed by primes = A124283. Primes indexed by 3-almost primes = A124268. 3-almost primes indexed by primes = A124269. prime(3almostprime(n)) - 3almostprime(prime(n)) = A124270. See also A106349 Primes indexed by semiprimes. See also A106350 Semiprimes indexed by primes. See also A122824 Prime(semiprime(n)) - semiprime(prime(n)).

Cf. A000040, A014613, A114414, A122824, A124269, A124270, A124282, A124283.

FourAlmostPrimePi[n_] := Sum[PrimePi[n/(Prime@i*Prime@j*Prime@k)] - k + 1, {i, PrimePi[n^(1/4)]}, {j, i, PrimePi[(n/Prime@i)^(1/3)]}, {k, j, PrimePi@ Sqrt[n/(Prime@i*Prime@j)]}];
FourAlmostPrime[n_] := Block[{e = Floor[Log[2, n] + 1], a, b}, a = 2^e; Do[b = 2^p; While[ FourAlmostPrimePi@a < n, a = a + b]; a = a - b/2, {p, e, 0, -1}]; a + b/2];
Table[ Prime@ FourAlmostPrime@ n - FourAlmostPrime@ Prime@ n, {n, 52}]

from math import isqrt
from sympy import primepi, primerange, integer_nthroot, prime
def A124284(n):
    def f(x): return int(x-sum(primepi(x//(k*m*r))-c for a,k in enumerate(primerange(integer_nthroot(x,4)[0]+1)) for b,m in enumerate(primerange(k,integer_nthroot(x//k,3)[0]+1),a) for c,r in enumerate(primerange(m,isqrt(x//(k*m))+1),b)))
    m, k = n, f(n)+n
    while m != k:
        m, k = k, f(k)+n
    r, k = (p:=prime(n)), f(p)+p
    while r != k:
        r, k = k, f(k)+p
    return prime(m)-r # Chai Wah Wu, Aug 17 2024

a(n) = prime(4almostprime(n)) - 4almostprime(prime(n)) = A000040(A014613(n)) -A014613(A000040(n)).

More terms from Robert G. Wilson v, Aug 31 2007

A124309 5-almost primes indexed by primes.

Original entry on oeis.org

48, 72, 108, 120, 180, 208, 270, 280, 368, 420, 450, 520, 592, 612, 660, 700, 760, 828, 920, 952, 976, 1032, 1064, 1128, 1242, 1288, 1323, 1372, 1380, 1428, 1575, 1624, 1674, 1700, 1752, 1768, 1880, 1976, 2028, 2096, 2178, 2196, 2312, 2328, 2384, 2394, 2475

Offset: 1

Jonathan Vos Post, Oct 25 2006

			a(1) = 5almostprime(prime(1)) = 5almostprime(2) = 48 = 2^4 * 3.
a(2) = 5almostprime(prime(2)) = 5almostprime(3) = 72 = 2^3 * 3^2.
a(3) = 5almostprime(prime(3)) = 5almostprime(5) = 108 = 2^2 * 3^3.

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A124308 Primes indexed by 5-almost primes. A124310 prime(5almostprime(n)) - 5almostprime(prime(n)). 4-almost primes indexed by primes = A124283. prime(4almostprime(n)) - 4almostprime(prime(n)) = A124284. Primes indexed by 3-almost primes = A124268. 3-almost primes indexed by primes = A124269. prime(3almostprime(n)) - 3almostprime(prime(n)) = A124270. See also A106349 Primes indexed by semiprimes. See also A106350 Semiprimes indexed by primes. See also A122824 Prime(semiprime(n)) - semiprime(prime(n)). Commutator [A000040, A001358] at n.

Cf. A000040, A014614, A114405, A114415, A124282-A124284, A124309.

list(lim)=my(v=List(),u=v); forprime(p=2,lim\16, forprime(q=2,min(lim\(8*p),p), forprime(r=2,min(lim\(4*p*q),q), forprime(s=2,min(lim\(2*p*q*r),r), forprime(t=2,min(lim\(p*q*r*s),s), listput(v,p*q*r*s*t)))))); v=Set(v); forprime(p=2,#v, listput(u,v[p])); v=0; Vec(u) \\ Charles R Greathouse IV, Feb 10 2017

a(n) = 5almostprime(prime(n)) = A014614(A000040(n)).

a(16)-a(47) from Giovanni Resta, Jun 13 2016

A124308 Primes indexed by 5-almost primes.

Original entry on oeis.org

131, 223, 359, 409, 593, 613, 659, 953, 997, 1049, 1069, 1223, 1283, 1543, 1601, 1693, 1733, 1747, 1811, 1987, 2003, 2069, 2503, 2593, 2693, 2713, 2789, 2801, 2903, 3079, 3181, 3221, 3301, 3323, 3541, 3571, 3727, 4003, 4127, 4283

Offset: 1

Jonathan Vos Post, Oct 25 2006

			a(1) = prime(5almostprime(1)) = prime(32 = 2^5) = 131.
a(2) = prime(5almostprime(2)) = prime(48 = 2^4 * 3) = 223.
a(3) = prime(5almostprime(3)) = prime(72 = 2^3 * 3^2) = 359.
a(4) = prime(5almostprime(4)) = prime(80 = 2^4 * 5) = 409.

Cf. A124309 5-almost primes indexed by primes. A124310 prime(5almostprime(n)) - 5almostprime(prime(n)). 4-almost primes indexed by primes = A124283. prime(4almostprime(n)) - 4almostprime(prime(n)) = A124284. Primes indexed by 3-almost primes = A124268. 3-almost primes indexed by primes = A124269. prime(3almostprime(n)) - 3almostprime(prime(n)) = A124270. See also A106349 Primes indexed by semiprimes. See also A106350 Semiprimes indexed by primes. See also A122824 Prime(semiprime(n)) - semiprime(prime(n)). Commutator [A000040, A001358] at n.

Cf. A000040, A014614, A114405, A114415, A122824, A124269, A124270, A124282-A124284, A124309, A124310.

Prime[#]&/@Select[Range[600],PrimeOmega[#]==5&] (* Harvey P. Dale, Nov 20 2015 *)

a(n) = prime(5almostprime(n)) = A000040(A014614(n)). {p such that p is prime and omega(primepi(p)) = 5} = {p such that p is in A000040 and A001222(A000720(p)) = 5}.

A124317 Semiprimes indexed by 3-almost primes.

Original entry on oeis.org

22, 34, 51, 57, 82, 85, 87, 123, 133, 134, 146, 158, 201, 205, 209, 214, 221, 226, 237, 295, 305, 309, 321, 327, 341, 361, 365, 371, 394, 395, 413, 447, 478, 481, 497, 501, 529, 533, 543, 545, 551, 554, 559, 583, 597, 614, 623, 635, 689, 699, 734, 763, 766

Offset: 1

Jonathan Vos Post, Oct 26 2006

Note that a(10)-a(9) = a(30)-a(29) = 1, achieving the minimum possible, due to a combination of the appropriate semiprime gap (A065516) and 3-almost prime gap (A114403).

			a(1) = semiprime(3almostprime(1)) = semiprime(8 = 2^3) = 22 = 2 * 11.
a(2) = semiprime(3almostprime(2)) = semiprime(12 = 2^2 * 3) = 34 = 2 * 17.
a(3) = semiprime(3almostprime(3)) = semiprime(18 = 2 * 3^2) = 51 = 3 * 17.

Giovanni Resta, Table of n, a(n) for n = 1..5000

Cf. A124318 3-almost primes indexed by semiprimes. A124319 semiprime(3almostprime(n)) - 3almostprime(semiprime(n)). A124308 Primes indexed by 5-almost primes. A124309 5-almost primes indexed by primes. A124310 prime(5almostprime(n)) - 5almostprime(prime(n)). 4-almost primes indexed by primes = A124283. prime(4almostprime(n)) - 4almostprime(prime(n)) = A124284. Primes indexed by 3-almost primes = A124268. 3-almost primes indexed by primes = A124269. prime(3almostprime(n)) - 3almostprime(prime(n)) = A124270. See also A106349 Primes indexed by semiprimes. See also A106350 Semiprimes indexed by primes. See also A122824 Prime(semiprime(n)) - semiprime(prime(n)). Commutator [A000040, A001358] at n.

Cf. A000040, A001358, A014612, A065516, A114403, A122824, A124269, A124270, A124282-A124284, A124309, A124310, A124318, A124319.

p[k_] := Select[Range[1000], PrimeOmega[#] == k &]; p[2][[Take[p[3], 60]]] (* Giovanni Resta, Jun 13 2016 *)

from math import isqrt
from sympy import primepi, primerange, integer_nthroot
def A124317(n):
    def f(x): return int(x-sum(primepi(x//(k*m))-b for a,k in enumerate(primerange(integer_nthroot(x,3)[0]+1)) for b,m in enumerate(primerange(k,isqrt(x//k)+1),a)))
    def g(x): return int(x+((t:=primepi(s:=isqrt(x)))*(t-1)>>1)-sum(primepi(x//k) for k in primerange(1, s+1)))
    m, k = n, f(n)+n
    while m != k:
        m, k = k, f(k)+n
    r, k = m, g(m)+m
    while r != k:
        r, k = k, g(k)+m
    return r # Chai Wah Wu, Aug 17 2024

a(n) = semiprime(3almostprime(n)) = A001358(A014612(n)).

Data corrected by Giovanni Resta, Jun 13 2016

A124318 3-almost primes indexed by semiprimes.

Original entry on oeis.org

20, 28, 44, 45, 66, 68, 98, 99, 110, 114, 147, 148, 153, 165, 170, 188, 207, 222, 238, 244, 245, 261, 273, 284, 310, 322, 343, 356, 357, 363, 374, 387, 388, 399, 429, 438, 465, 475, 477, 494, 498, 506, 531, 549, 555, 590, 595, 596, 602, 603, 628, 639, 642

Offset: 1

Jonathan Vos Post, Oct 26 2006

			a(1) = 3almostprime(semiprime(1)) = 3almostprime(4 = 2^2) = 20 = 2^2 * 5.
a(2) = 3almostprime(semiprime(2)) = 3almostprime(6 = 2 * 3) = 28 = 2^2 * 7.
a(3) = 3almostprime(semiprime(3)) = 3almostprime(9 = 3^2) = 44 = 2^2 * 11.
a(4) = 3almostprime(semiprime(4)) = 3almostprime(10 = 2 * 5) = 45 = 3^2 * 5.

Cf. A124317 Semiprimes indexed by 3-almost primes. A124318 3-almost primes indexed by semiprimes. A124319 semiprime(3almostprime(n)) - 3almostprime(semiprime(n)). A124308 Primes indexed by 5-almost primes. A124309 5-almost primes indexed by primes. A124310 prime(5almostprime(n)) - 5almostprime(prime(n)). 4-almost primes indexed by primes = A124283. prime(4almostprime(n)) - 4almostprime(prime(n)) = A124284. Primes indexed by 3-almost primes = A124268. 3-almost primes indexed by primes = A124269. prime(3almostprime(n)) - 3almostprime(prime(n)) = A124270. See also A106349 Primes indexed by semiprimes. See also A106350 Semiprimes indexed by primes. See also A122824 Prime(semiprime(n)) - semiprime(prime(n)). Commutator [A000040, A001358] at n.

Cf. A000040, A001358, A014612, A065516, A114403, A122824, A124269, A124270, A124282-A124284, A124309, A124310, A124317, A124319.

p[k_] := Select[Range[1000], PrimeOmega[#] == k &]; p[3][[Take[p[2], 60]]] (* Giovanni Resta, Jun 13 2016 *)

from math import isqrt
from sympy import primepi, primerange, integer_nthroot
def A124318(n):
    def g(x): return int(x-sum(primepi(x//(k*m))-b for a,k in enumerate(primerange(integer_nthroot(x,3)[0]+1)) for b,m in enumerate(primerange(k,isqrt(x//k)+1),a)))
    def f(x): return int(x+((t:=primepi(s:=isqrt(x)))*(t-1)>>1)-sum(primepi(x//k) for k in primerange(1, s+1)))
    m, k = n, f(n)+n
    while m != k:
        m, k = k, f(k)+n
    r, k = m, g(m)+m
    while r != k:
        r, k = k, g(k)+m
    return r # Chai Wah Wu, Aug 17 2024

a(n) = 3almostprime(semiprime(n)) = A014612(A001358(n)).

a(22)-a(53) from Giovanni Resta, Jun 13 2016

A124319 Semiprime(3almostprime(n))-3almostprime(semiprime(n)). Commutator[A001358, A014612] at n.

Original entry on oeis.org

2, 6, 7, 12, 16, 17, -11, 24, 23, 20, -1, 10, 48, 40, 39, 26, 14, 4, -1, 51, 60, 48, 48, 43, 31, 39, 22, 15, 37, 32, 39, 60, 90, 82, 68, 63, 64, 58, 66, 51, 53, 48, 28, 34, 42, 24, 28, 39, 87, 96, 106, 124, 124, 135, 131, 131, 88, 91, 72, 96, 103, 83, 83, 81, 91

Offset: 1

Jonathan Vos Post, Oct 26 2006

			a(1) = semiprime(3almostprime(1)) - 3almostprime(semiprime(1)) = 22 - 20 = 2.
a(2) = semiprime(3almostprime(2)) - 3almostprime(semiprime(2)) = 34 - 28 = 6.
a(3) = semiprime(3almostprime(3)) - 3almostprime(semiprime(3)) = 51 - 44 = 7.
a(4) = semiprime(3almostprime(4)) - 3almostprime(semiprime(4)) = 57 - 45 = 12.
a(7) = semiprime(3almostprime(7)) - 3almostprime(semiprime(7)) = 87 - 98 = -11, which is the first negative value in the commutators we have seen in these related set of sequences, exposing an incorrect assumption.

Cf. A124317 Semiprimes indexed by 3-almost primes. A124318 3-almost primes indexed by semiprimes. A124319 semiprime(3almostprime(n)) - 3almostprime(semiprime(n)). A124308 Primes indexed by 5-almost primes. A124309 5-almost primes indexed by primes. A124310 prime(5almostprime(n)) - 5almostprime(prime(n)). 4-almost primes indexed by primes = A124283. prime(4almostprime(n)) - 4almostprime(prime(n)) = A124284. Primes indexed by 3-almost primes = A124268. 3-almost primes indexed by primes = A124269. prime(3almostprime(n)) - 3almostprime(prime(n)) = A124270. See also A106349 Primes indexed by semiprimes. See also A106350 Semiprimes indexed by primes. See also A122824 Prime(semiprime(n)) - semiprime(prime(n)). Commutator [A000040, A001358] at n.

Cf. A000040, A001358, A014612, A065516, A114403, A122824, A124269, A124270, A124282-A124284, A124309, A124310, A124317, A124318.

p[k_] := p[k] = Select[Range[1000], PrimeOmega[#] == k &]; p[2][[ Take[p[3], 70]]] - p[3][[Take[p[2], 70]]] (* Giovanni Resta, Jun 13 2016 *)

from math import isqrt
from sympy import primepi, primerange, integer_nthroot
def A124319(n):
    def f(x): return int(x-sum(primepi(x//(k*m))-b for a,k in enumerate(primerange(integer_nthroot(x,3)[0]+1)) for b,m in enumerate(primerange(k,isqrt(x//k)+1),a)))
    def g(x): return int(x+((t:=primepi(s:=isqrt(x)))*(t-1)>>1)-sum(primepi(x//k) for k in primerange(1, s+1)))
    def A001358(n):
        m, k = n, g(n)+n
        while m != k:
            m, k = k, g(k)+n
        return m
    m, k = n, f(n)+n
    while m != k:
        m, k = k, f(k)+n
    r, k = (p:=A001358(n)), f(p)+p
    while r != k:
        r, k = k, f(k)+p
    return A001358(m)-r # Chai Wah Wu, Aug 17 2024

a(18) corrected and a(22)-a(65) from Giovanni Resta, Jun 13 2016

cp's OEIS Frontend

A124268 Primes indexed by 3-almost primes.

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A124269 3-almost primes indexed by primes.

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A124282 Primes indexed by 4-almost primes.

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A124283 4-almost primes indexed by primes.

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A124284 Prime(4almostprime(n))-4almostprime(prime(n)). Commutator [A000040,A014613] at n.

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A124309 5-almost primes indexed by primes.

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Extensions

A124308 Primes indexed by 5-almost primes.

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Mathematica

Formula

A124317 Semiprimes indexed by 3-almost primes.

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