A370495 Oblong numbers of the form (k-1)*k where k is the product of an even number of distinct primes.
0, 30, 90, 182, 210, 420, 462, 650, 1056, 1122, 1190, 1406, 1482, 2070, 2550, 2970, 3192, 3306, 3782, 4160, 4692, 5402, 5852, 6642, 7140, 7310, 7482, 8190, 8556, 8742, 8930, 11130, 12210, 13110, 13806, 14042, 14762, 15006, 16512, 17556, 17822, 19740, 20022, 20306
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 A370495(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-1+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(2,x.bit_length(),2))) return (k:=bisection(f,n,n))*(k-1) # Chai Wah Wu, Jan 28 2025