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%I A104350 #45 Oct 23 2024 06:50:37
%S A104350 1,2,6,12,60,180,1260,2520,7560,37800,415800,1247400,16216200,
%T A104350 113513400,567567000,1135134000,19297278000,57891834000,1099944846000,
%U A104350 5499724230000,38498069610000,423478765710000,9740011611330000
%N A104350 Partial products of largest prime factors of numbers <= n.
%C A104350 Partial Products of A006530: a(n) = Product_{k=1..n} A006530(k).
%C A104350 a(n) = a(n-1)*A006530(n) for n>1, a(1) = 1;
%C A104350 A020639(a(n)) = A040000(n-1), A006530(a(n)) = A007917(n) for n>1.
%C A104350 A001221(a(n)) = A000720(n), A001222(a(n)) = A001477(n-1).
%C A104350 A007947(a(n)) = A034386(n).
%C A104350 a(n) = A000142(n) / A076928(n). [Corrected by _Franklin T. Adams-Watters_, Oct 30 2006]
%C A104350 In decimal representation: A104351(n) = number of digits of a(n), A104355(n) = number of trailing zeros of a(n).
%C A104350 A104357(n) = a(n) - 1, A104365(n) = a(n) + 1.
%D A104350 Gérald Tenenbaum, Introduction à la théorie analytique et probabiliste des nombres, Publ. Inst. Elie Cartan, Vol. 13, Nancy, 1990.
%H A104350 Charles R Greathouse IV, <a href="/A104350/b104350.txt">Table of n, a(n) for n = 1..641</a>
%H A104350 Romeo Meštrović, <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], 2012-2018.
%H A104350 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GreatestPrimeFactor.html">Greatest Prime Factor</a>.
%H A104350 Reinhard Zumkeller, <a href="/A104350/a104350.txt">Products of largest prime factors of numbers <= n</a>.
%F A104350 log(a(n)) = c * n * log(n) + c * (1-gamma) * n + O(n * exp(-log(n)^(3/8-eps))), where c is the Golomb-Dickman constant (A084945) and gamma is Euler's constant (A001620) (Tenenbaum, 1990). - _Amiram Eldar_, May 21 2021
%t A104350 A104350[n_] := Product[FactorInteger[k][[-1, 1]], {k, 1, n}]; Table[A104350[n], {n, 30}] (* _G. C. Greubel_, May 09 2017 *)
%t A104350 FoldList[Times,Table[FactorInteger[n][[-1,1]],{n,30}]] (* _Harvey P. Dale_, May 25 2023 *)
%o A104350 (Haskell)
%o A104350 a104350 n = a104350_list !! (n-1)
%o A104350 a104350_list = scanl1 (*) a006530_list
%o A104350 -- _Reinhard Zumkeller_, Apr 10 2014
%o A104350 (PARI) gpf(n)=my(f=factor(n)[,1]); f[#f]
%o A104350 a(n)=prod(i=2,n,gpf(i)) \\ _Charles R Greathouse IV_, Apr 29 2015
%o A104350 (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 A104350 Cf. A000142, A002110, A006530, A007947, A020639, A046670, A072486, A076928, A104351, A104355, A104357, A104365.
%Y A104350 Cf. A001620, A084945.
%K A104350 nonn
%O A104350 1,2
%A A104350 _Reinhard Zumkeller_, Mar 06 2005
%E A104350 More terms from _David Wasserman_, Apr 24 2008

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