A074167 Product of prime divisors of composite numbers between consecutive primes.

1, 2, 6, 60, 6, 420, 6, 4620, 32760, 30, 471240, 14820, 42, 15180, 556920, 15273720, 30, 11171160, 164220, 6, 253333080, 2460, 587636280, 625757605200, 4620, 102, 289380, 6, 170940, 26848135265397670224000, 33540, 599888520, 138, 39560762839197600, 30

Offset: 1

Author

Amarnath Murthy, Aug 30 2002

Keywords

• nonn

Examples

			a(4) = product of prime factors of composite numbers between 7 and 11 = 2 * 3 * (2 * 5) = 60.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A007947, A059960, A076978.

Programs

Maple

a:= n-> mul(mul(i[1], i=ifactors(j)[2]), j=ithprime(n)+1..ithprime(n+1)-1):
seq(a(n), n=1..40);  # Alois P. Heinz, May 29 2022

Mathematica

Array[Times @@ Flatten@ Map[FactorInteger[#][[All, 1]] &, Range[#1 + 1, #2 - 1]] & @@ Prime[{#, # + 1}] &, 35] (* Michael De Vlieger, May 29 2022 *)

PARI

a(n) = my(p=1); forcomposite(c=prime(n), prime(n+1), p*=factorback(factorint(c)[, 1])); p; \\ Michel Marcus, May 29 2022

Formula

a(n) = 6 <=> A000040(n) in { A059960 }. - Alois P. Heinz, May 29 2022

Extensions

Corrected and extended by Joshua Zucker, May 08 2006

Offset corrected by Alois P. Heinz, May 29 2022