OFFSET
1,2
COMMENTS
Equivalently, the largest squarefree number that divides the product of composite numbers between successive primes.
From Robert G. Wilson v, Dec 02 2020: (Start)
All terms greater than one are even.
Omega(a(n)): 0, 1, 2, 3, 2, 4, 2, 5, 5, 3, 6, 5, 3, 5, 6, 7, 3, 7, 6, 2, 8, 4, 8, 9, 5, ..., .
Records: 1, 2, 6, 30, 210, 2310, 2730, 39270, 46410, 1272810, 21111090, ..., (2*A354218).
Factored: 1, 2, 2*3, 2*3*5, 2*3*5*7, 2*3*5*7*11, 2*3*5*7*13, 2*3*5*7*11*17, 2*3*5*7*13*17, 2*3*5*7*11*19*29, ..., .
(End)
LINKS
Robert G. Wilson v, Table of n, a(n) for n = 1..10000
FORMULA
From Michel Marcus, May 29 2022: (Start)
EXAMPLE
a(4) = product of prime divisors of the product of composite numbers between 7 and 11 = 2 * 3 * 5 = 30.
a(5)=6 because 12 is the only composite number between the 5th and the 6th primes (11 and 13) and largest squarefree divisor of 12 is 6.
MAPLE
with(numtheory): b:=proc(j) if issqrfree(j) then j else fi end: a:=proc(n) local B, BB: B:=divisors(product(i, i=ithprime(n)+1..ithprime(n+1)-1)): BB:=(seq(b(B[j]), j=1..nops(B))): max(BB); end: seq(a(n), n=1..33); # Emeric Deutsch, Jul 28 2006
MATHEMATICA
f[n_] := Times @@ (First@# & /@ FactorInteger[Times @@ Range[Prime[n] + 1, Prime[n + 1] - 1]]); Array[f, 50] (* Robert G. Wilson v, Dec 02 2020 *)
PROG
(PARI) a(n) = my(p=1); forcomposite(c=prime(n), prime(n+1), p*=c); factorback(factorint(p)[, 1]); \\ Michel Marcus, May 29 2022
(Python) from sympy import sieve as p, primefactors
def A076978(n):
result = 1
for composites in range(p[n]+1, p[n+1]):
for primefactor in primefactors(composites):
if result % primefactor != 0: result *= primefactor
return result # Karl-Heinz Hofmann, May 30 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Oct 23 2002
EXTENSIONS
More terms from Emeric Deutsch, Jul 28 2006
More terms from Robert G. Wilson v, Dec 02 2020
Entry revised by N. J. A. Sloane, Dec 02 2020
STATUS
approved