cp's OEIS Frontend

A385631 Products of five consecutive integers whose prime divisors are consecutive primes starting at 2.

%I A385631 #8 Jul 09 2025 16:36:07
%S A385631 120,720,2520,6720,15120,30240,55440,240240,360360
%N A385631 Products of five consecutive integers whose prime divisors are consecutive primes starting at 2.
%e A385631 a(1) = 120 = 1*2*3*4*5 = 2^3 * 3^1 * 5^1.
%e A385631 a(2) = 720 = 2*3*4*5*6 = 2^4 * 3^2 * 5^1.
%e A385631 a(3) = 2520 = 3*4*5*6*7 = 2^3 * 3^2 * 5^1 * 7^1.
%e A385631 a(4) = 6720 = 4*5*6*7*8 = 2^6 * 3^1 * 5^1 * 7^1.
%e A385631 a(5) = 15120 = 5*6*7*8*9 = 2^4 * 3^3 * 5^1 * 7^1.
%e A385631 a(6) = 30240 = 6*7*8*9*10 = 2^5 * 3^3 * 5^1 * 7^1.
%e A385631 a(7) = 55440 = 7*8*9*10*11 = 2^4 * 3^2 * 5^1 * 7^1 * 11^1.
%e A385631 a(8) = 240240 = 10*11*12*13*14 = 2^4 * 3^1 * 5^1 * 7^1 * 11^1 * 13^1.
%e A385631 a(9) = 360360 = 11*12*13*14*15 = 2^3 * 3^2 * 5^1 * 7^1 * 11^1 * 13^1.
%t A385631 Select[(#*(# + 1)*(# + 2)*(# + 3)*(# + 4)) & /@ Range[12], PrimePi[(f = FactorInteger[#1])[[-1, 1]]] == Length[f] &] (* _Amiram Eldar_, Jul 05 2025 *)
%o A385631 (Python)
%o A385631 from sympy import prime, primefactors
%o A385631 def is_pi_complete(n): # Check for complete set of
%o A385631     factors = primefactors(n) # prime factors
%o A385631     return factors[-1] == prime(len(factors))
%o A385631 def aupto(limit):
%o A385631     result = []
%o A385631     for i in range(1, limit+1):
%o A385631         n = i * (i+1) * (i+2) * (i+3) * (i+4)
%o A385631         if is_pi_complete(n):
%o A385631             result.append(n)
%o A385631     return result
%o A385631 print(aupto(1000))
%Y A385631 Intersection of A052787 and A055932.
%Y A385631 Cf. A217056, A385189, A385415.
%K A385631 nonn,fini,full
%O A385631 1,1
%A A385631 _Ken Clements_, Jul 05 2025