A104355 -id:A104355 - cp's OEIS frontend

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

1, 2, 6, 12, 60, 180, 1260, 2520, 7560, 37800, 415800, 1247400, 16216200, 113513400, 567567000, 1135134000, 19297278000, 57891834000, 1099944846000, 5499724230000, 38498069610000, 423478765710000, 9740011611330000

Offset: 1

Reinhard Zumkeller, Mar 06 2005

nonn

Partial Products of A006530: a(n) = Product_{k=1..n} A006530(k).
a(n) = a(n-1)*A006530(n) for n>1, a(1) = 1;
A020639(a(n)) = A040000(n-1), A006530(a(n)) = A007917(n) for n>1.
A001221(a(n)) = A000720(n), A001222(a(n)) = A001477(n-1).
A007947(a(n)) = A034386(n).
a(n) = A000142(n) / A076928(n). [Corrected by Franklin T. Adams-Watters, Oct 30 2006]
In decimal representation: A104351(n) = number of digits of a(n), A104355(n) = number of trailing zeros of a(n).
A104357(n) = a(n) - 1, A104365(n) = a(n) + 1.

Gérald Tenenbaum, Introduction à la théorie analytique et probabiliste des nombres, Publ. Inst. Elie Cartan, Vol. 13, Nancy, 1990.

Charles R Greathouse IV, Table of n, a(n) for n = 1..641
Romeo Meštrović, Euclid's theorem on the infinitude of primes: a historical survey of its proofs (300 BC--2012) and another new proof, arXiv preprint, arXiv:1202.3670 [math.HO], 2012-2018.
Eric Weisstein's World of Mathematics, Greatest Prime Factor.
Reinhard Zumkeller, Products of largest prime factors of numbers <= n.

Cf. A000142, A002110, A006530, A007947, A020639, A046670, A072486, A076928, A104351, A104355, A104357, A104365.

Cf. A001620, A084945.

a104350 n = a104350_list !! (n-1)
a104350_list = scanl1 (*) a006530_list
-- Reinhard Zumkeller, Apr 10 2014

A104350[n_] := Product[FactorInteger[k][[-1, 1]], {k, 1, n}]; Table[A104350[n], {n, 30}] (* G. C. Greubel, May 09 2017 *)
FoldList[Times,Table[FactorInteger[n][[-1,1]],{n,30}]] (* Harvey P. Dale, May 25 2023 *)

gpf(n)=my(f=factor(n)[,1]); f[#f]
a(n)=prod(i=2,n,gpf(i)) \\ Charles R Greathouse IV, Apr 29 2015

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

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

More terms from David Wasserman, Apr 24 2008

A104356 Smallest m such that A104350(m) has exactly n trailing zeros in decimal representation.

Original entry on oeis.org

1, 5, 10, 15, 20, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912, 1073741824, 2147483648

Offset: 0

Reinhard Zumkeller, Mar 06 2005

A104355(a(n)) = n and A104355(m) < n for m < a(n).

a(n) = if n=0 then 1 else (if n<5 then 5*n else 2^n).

cp's OEIS Frontend

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

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