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

120, 720, 2520, 6720, 15120, 30240, 55440, 240240, 360360

Offset

1,1

Links

Table of n, a(n) for n=1..9.

Example

a(1) = 120 = 1*2*3*4*5 = 2^3 * 3^1 * 5^1.
a(2) = 720 = 2*3*4*5*6 = 2^4 * 3^2 * 5^1.
a(3) = 2520 = 3*4*5*6*7 = 2^3 * 3^2 * 5^1 * 7^1.
a(4) = 6720 = 4*5*6*7*8 = 2^6 * 3^1 * 5^1 * 7^1.
a(5) = 15120 = 5*6*7*8*9 = 2^4 * 3^3 * 5^1 * 7^1.
a(6) = 30240 = 6*7*8*9*10 = 2^5 * 3^3 * 5^1 * 7^1.
a(7) = 55440 = 7*8*9*10*11 = 2^4 * 3^2 * 5^1 * 7^1 * 11^1.
a(8) = 240240 = 10*11*12*13*14 = 2^4 * 3^1 * 5^1 * 7^1 * 11^1 * 13^1.
a(9) = 360360 = 11*12*13*14*15 = 2^3 * 3^2 * 5^1 * 7^1 * 11^1 * 13^1.

Mathematica

Select[(#*(# + 1)*(# + 2)*(# + 3)*(# + 4)) & /@ Range[12], PrimePi[(f = FactorInteger[#1])[[-1, 1]]] == Length[f] &] (* Amiram Eldar, Jul 05 2025 *)

Prog

(Python)
from sympy import prime, primefactors
def is_pi_complete(n): # Check for complete set of
    factors = primefactors(n) # prime factors
    return factors[-1] == prime(len(factors))
def aupto(limit):
    result = []
    for i in range(1, limit+1):
        n = i * (i+1) * (i+2) * (i+3) * (i+4)
        if is_pi_complete(n):
            result.append(n)
    return result
print(aupto(1000))

Crossrefs

Intersection of A052787 and A055932.

Cf. A217056, A385189, A385415.

Sequence in context: A306602 A300299 A052787 * A292970 A052769 A179724

Adjacent sequences: A385628 A385629 A385630 * A385632 A385633 A385634

Keyword

nonn,fini,full

Author

Ken Clements, Jul 05 2025

Status

approved