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

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] (* Jean-Fran├žois 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

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Last modified August 3 08:21 EDT 2021. Contains 346435 sequences. (Running on oeis4.)