A056831 -id:A056831 - cp's OEIS frontend

A079615 Product of all distinct prime factors of all composite numbers between n-th prime and next prime.

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

Offset: 2

Reinhard Zumkeller, Jan 29 2003

a(n) = A007947(A056831(n)), squarefree kernel of least common multiple of composite numbers between n-th prime and next prime.
Note that each term is a product of distinct primes. - T. D. Noe, May 19 2007
Equals A076978 without its first term. - R. J. Mathar, Sep 19 2008
Same for A074168. - Georg Fischer, Oct 06 2018
For n > 2, a(n) is of the form 2*3*r, where r is relatively prime to 6. Therefore, for every n > 2, a(n) is a Zumkeller number (see Corollary 5, Rao/Peng link). - Ivan N. Ianakiev, Jan 24 2020

			n=9: factorizations of numbers between 23=A000040(9) and 29=A000040(10) are 24=3*2^3, 25=5^2, 26=13*2 and 27=3^3, therefore a(9) = 2*3*5*7*13 = 2730.

T. D. Noe, Table of n, a(n) for n = 2..1000
K. P. S. Bhaskara Rao and Yuejian Peng, On Zumkeller Numbers, Journal of Number Theory, Volume 133, Issue 4, April 2013, pp. 1135-1155.

Cf. A005117, A002110, A083207.

a[n_] := (p = Prime[n]; s = Select[Table[k, {k, p, NextPrime[p]}], ! PrimeQ[#] &]; Times @@ ((FactorInteger /@ s // Flatten[#, 1] &)[[All, 1]] // Union)); a /@ Range[2, 35] (* Jean-François Alcover, Jul 13 2011 *)
Table[Times@@Union[Flatten[Transpose[FactorInteger[#]][[1]]&/@ (Range[ Prime[ n]+1, NextPrime[Prime[n]]-1])]],{n,2,50}] (* Harvey P. Dale, Oct 10 2011 *)

Corrected by T. D. Noe, May 19 2007

A362296 Greatest common divisor of composite numbers between the n-th and (n+1)st primes.

Original entry on oeis.org

4, 6, 1, 12, 1, 18, 1, 1, 30, 1, 1, 42, 1, 1, 1, 60, 1, 1, 72, 1, 1, 1, 1, 1, 102, 1, 108, 1, 1, 1, 1, 138, 1, 150, 1, 1, 1, 1, 1, 180, 1, 192, 1, 198, 1, 1, 1, 228, 1, 1, 240, 1, 1, 1, 1, 270, 1, 1, 282, 1, 1, 1, 312, 1, 1, 1, 1, 348, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset: 2

Chai Wah Wu, Apr 15 2023

nonn

Winston de Greef, Table of n, a(n) for n = 2..10000

Cf. A056831 (LCM), A061214 (product).

a(n) = gcd([prime(n)+1..prime(n+1)-1]); \\ Michel Marcus, Apr 16 2023

from sympy import prime, isprime
def A362296(n): return m-1 if isprime(m:=prime(n)+2) else 1

For n > 1, a(n)=prime(n)+1 if and only if prime(n+1)=prime(n)+2 and a(n)=1 otherwise.

cp's OEIS Frontend

A079615 Product of all distinct prime factors of all composite numbers between n-th prime and next prime.

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