OFFSET
2,1
COMMENTS
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
LINKS
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.
EXAMPLE
MATHEMATICA
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 *)
CROSSREFS
KEYWORD
nonn,nice
AUTHOR
Reinhard Zumkeller, Jan 29 2003
EXTENSIONS
Corrected by T. D. Noe, May 19 2007
STATUS
approved