A370494 Oblong numbers of the form (k-1)*k where k is the product of an odd number of distinct primes.
2, 6, 20, 42, 110, 156, 272, 342, 506, 812, 870, 930, 1332, 1640, 1722, 1806, 2162, 2756, 3422, 3660, 4290, 4422, 4830, 4970, 5256, 6006, 6162, 6806, 7832, 9312, 10100, 10302, 10506, 10920, 11342, 11772, 11990, 12656, 12882, 16002, 16770, 17030, 18632, 18906, 19182
Offset: 1
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
Table[n*(n - 1), {n, Select[Range[150], MoebiusMu[#] == -1 &]}] -
PARI
lista(kmax) = forsquarefree(k=1, kmax, if(moebius(k) == -1, print1(k[1]*(k[1]-1), ", ")));
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Python
from math import isqrt, prod from sympy import primerange, integer_nthroot, primepi def A370494(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 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(n+x-primepi(x)-sum(sum(primepi(x//prod(c[1] for c in a))-a[-1][0] for a in g(x,0,1,1,i)) for i in range(3,x.bit_length(),2))) return (k:=bisection(f,n,n))*(k-1) # Chai Wah Wu, Jan 28 2025