A335496 - OEIS

%I #11 Jul 10 2023 01:43:34

%S 23,871,5423,229955,13771373,558588875,21549990623,1325878234371,

%T 17040894859373,429205867309373

%N a(n) is the least odd number k such that Omega(k) = n, Omega(k+2) = n+1, and Omega(k+4) = n+2, where Omega(k) is the number of prime factors of k (A001222).

%C a(n) mod 81 for n = 1..8: {23, 61, 77, 77, 77, 77, 77, 0}.

%F a(n) >= A335498(n). - _Daniel Suteu_, Jul 08 2023

%e 23 is a term: 23 is a prime, 25=5*5 is a semiprime, 27=3*3*3 is a triprime.

%e 871 is a term: 871 = 13*67 (semiprime), 873 = 3*3*97 (triprime), 875 = 5*5*5*7 (quadprime).

%o (PARI)

%o generate(A, B, n, k) = A=max(A, 2^n); (f(m, p, n) = my(list=List()); if(n==1, forprime(q=max(p, ceil(A/m)), B\m, my(t=m*q); if(bigomega(t-4) == k && bigomega(t-2) == k+1, listput(list, t-4))), forprime(q=p, sqrtnint(B\m, n), list=concat(list, f(m*q, q, n-1)))); list); vecsort(Vec(f(1, 3, n)));

%o a(n) = my(x=2^n, y=2*x); while(1, my(v=generate(x, y, n+2, n)); if(#v >= 1, return(v[1])); x=y+1; y=2*x); \\ _Daniel Suteu_, Jul 08 2023

%Y Cf. A335498.

%K nonn,more

%O 1,1

%A _Zak Seidov_ and _Giovanni Resta_, Jun 11 2020

%E a(9)-a(10) from _Daniel Suteu_, Jul 08 2023