

A079615


Product of all distinct prime factors of all composite numbers between nth prime and next prime.


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
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

2,1


COMMENTS

a(n) = A007947(A056831(n)), squarefree kernel of least common multiple of composite numbers between nth 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. 11351155.


EXAMPLE

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.


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] (* JeanFrançois 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

Cf. A005117, A002110, A083207.
Sequence in context: A181812 A330648 A074168 * A076978 A117213 A127797
Adjacent sequences: A079612 A079613 A079614 * A079616 A079617 A079618


KEYWORD

nonn,nice


AUTHOR

Reinhard Zumkeller, Jan 29 2003


EXTENSIONS

Corrected by T. D. Noe, May 19 2007


STATUS

approved



