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A076978 Product of the distinct primes dividing the product of composite numbers between consecutive primes. 4
1, 2, 6, 30, 6, 210, 6, 2310, 2730, 30, 39270, 7410, 42, 7590, 46410, 1272810, 30, 930930, 82110, 6, 21111090, 1230, 48969690, 1738215570, 2310, 102, 144690, 6, 85470, 29594505363092670, 16770, 49990710, 138, 7849357706190, 30, 300690390, 20223210, 1122990, 37916970 (list; graph; refs; listen; history; text; internal format)
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, ..., .

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

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 *)

CROSSREFS

Cf. A074167.

Sequence in context: A330648 A074168 A079615 * A117213 A127797 A338441

Adjacent sequences:  A076975 A076976 A076977 * A076979 A076980 A076981

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

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Last modified July 31 08:38 EDT 2021. Contains 346369 sequences. (Running on oeis4.)