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A104350
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Partial products of largest prime factors of numbers <= n.
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28
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1, 2, 6, 12, 60, 180, 1260, 2520, 7560, 37800, 415800, 1247400, 16216200, 113513400, 567567000, 1135134000, 19297278000, 57891834000, 1099944846000, 5499724230000, 38498069610000, 423478765710000, 9740011611330000
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OFFSET
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1,2
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COMMENTS
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a(n) = a(n-1)*A006530(n) for n>1, a(1) = 1;
In decimal representation: A104351(n) = number of digits of a(n), A104355(n) = number of trailing zeros of a(n).
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REFERENCES
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Gérald Tenenbaum, Introduction à la théorie analytique et probabiliste des nombres, Publ. Inst. Elie Cartan, Vol. 13, Nancy, 1990.
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LINKS
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FORMULA
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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
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MATHEMATICA
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FoldList[Times, Table[FactorInteger[n][[-1, 1]], {n, 30}]] (* Harvey P. Dale, May 25 2023 *)
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PROG
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(Haskell)
a104350 n = a104350_list !! (n-1)
a104350_list = scanl1 (*) a006530_list
(PARI) gpf(n)=my(f=factor(n)[, 1]); f[#f]
(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
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CROSSREFS
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Cf. A000142, A002110, A006530, A007947, A020639, A046670, A072486, A076928, A104351, A104355, A104357, A104365.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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