A340316 Square array A(n,k), n>=1, k>=1, read by antidiagonals, where row n is the increasing list of all squarefree numbers with n primes.
2, 3, 6, 5, 10, 30, 7, 14, 42, 210, 11, 15, 66, 330, 2310, 13, 21, 70, 390, 2730, 30030, 17, 22, 78, 462, 3570, 39270, 510510, 19, 26, 102, 510, 3990, 43890, 570570, 9699690, 23, 33, 105, 546, 4290, 46410, 690690, 11741730, 223092870
Offset: 1
Examples
First six rows and columns:
2 3 5 7 11 13
6 10 14 15 21 22
30 42 66 70 78 102
210 330 390 462 510 546
2310 2730 3570 3990 4290 4830
30030 39270 43890 46410 51870 53130
Crossrefs
Programs
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Haskell
a340316 n k = a340316_row n !! (k-1) a340316_row n = [a005117_list !! k | k <- [0..], a072047_list !! k == n]
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Python
from math import prod, isqrt from sympy import prime, primerange, integer_nthroot, primepi def A340316_T(n,k): if n == 1: return prime(k) def g(x,a,b,c,m): yield from (((d,) for d in enumerate(primerange(b+1,isqrt(x//c)+1),a+1)) if m==2 else (((a2,b2),)+d for a2,b2 in enumerate(primerange(b+1,integer_nthroot(x//c,m)[0]+1),a+1) for d in g(x,a2,b2,c*b2,m-1))) def f(x): return int(k+x-sum(primepi(x//prod(c[1] for c in a))-a[-1][0] for a in g(x,0,1,1,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 return bisection(f) # Chai Wah Wu, Aug 31 2024
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