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A104350 Partial products of largest prime factors of numbers <= n. 27

%I

%S 1,2,6,12,60,180,1260,2520,7560,37800,415800,1247400,16216200,

%T 113513400,567567000,1135134000,19297278000,57891834000,1099944846000,

%U 5499724230000,38498069610000,423478765710000,9740011611330000

%N Partial products of largest prime factors of numbers <= n.

%C Partial Products of A006530: a(n)=Prod(A006530(k):1<=k<=n);

%C a(n) = a(n-1)*A006530(n) for n>1, a(1) = 1;

%C A020639(a(n))=A040000(n-1), A006530(a(n))=A007917(n) for n>1,

%C A001221(a(n))=A000720(n), A001222(a(n))=A001477(n-1);

%C A007947(a(n))=A034386(n);

%C a(n) = A000142(n) / A076928(n). [Corrected by _Franklin T. Adams-Watters_, Oct 30 2006]

%C In decimal representation: A104351(n) = number of digits of a(n), A104355(n) = number of trailing zeros of a(n);

%C A104357(n) = a(n) - 1, A104365(n) = a(n) + 1.

%H Charles R Greathouse IV, <a href="/A104350/b104350.txt">Table of n, a(n) for n = 1..641</a>

%H R. Mestrovic, <a href="http://arxiv.org/abs/1202.3670">Euclid's theorem on the infinitude of primes: a historical survey of its proofs (300 BC--2012) and another new proof</a>, arXiv preprint arXiv:1202.3670 [math.HO], 2012.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GreatestPrimeFactor.html">Greatest Prime Factor</a>

%H R. Zumkeller, <a href="/A104350/a104350.txt">Products of largest prime factors of numbers <= n</a>

%t A104350[n_] := Product[FactorInteger[k][[-1, 1]], {k, 1, n}]; Table[A104350[n], {n, 30}] (* _G. C. Greubel_, May 09 2017 *)

%o (Haskell)

%o a104350 n = a104350_list !! (n-1)

%o a104350_list = scanl1 (*) a006530_list

%o -- _Reinhard Zumkeller_, Apr 10 2014

%o (PARI) gpf(n)=my(f=factor(n)[,1]); f[#f]

%o a(n)=prod(i=2,n,gpf(i)) \\ _Charles R Greathouse IV_, Apr 29 2015

%o (PARI) first(n)=my(v=vector(n,i,1)); forfactored(k=2,n, v[k[1]]=v[k[1]-1]*vecmax(k[2][,1])); v \\ _Charles R Greathouse IV_, May 10 2017

%Y Cf. A046670, A000142, A002110, A072486.

%K nonn

%O 1,2

%A _Reinhard Zumkeller_, Mar 06 2005

%E More terms from _David Wasserman_, Apr 24 2008

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Last modified February 24 12:59 EST 2018. Contains 299623 sequences. (Running on oeis4.)