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A104350 Partial products of largest prime factors of numbers <= n. 27
1, 2, 6, 12, 60, 180, 1260, 2520, 7560, 37800, 415800, 1247400, 16216200, 113513400, 567567000, 1135134000, 19297278000, 57891834000, 1099944846000, 5499724230000, 38498069610000, 423478765710000, 9740011611330000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

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.

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..641

R. Mestrovic, 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.

Eric Weisstein's World of Mathematics, Greatest Prime Factor

R. Zumkeller, Products of largest prime factors of numbers <= n

MATHEMATICA

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

PROG

(Haskell)

a104350 n = a104350_list !! (n-1)

a104350_list = scanl1 (*) a006530_list

-- Reinhard Zumkeller, Apr 10 2014

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

a(n)=prod(i=2, n, gpf(i)) \\ Charles R Greathouse IV, Apr 29 2015

(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

CROSSREFS

Cf. A046670, A000142, A002110, A072486.

Sequence in context: A195307 A101657 A104371 * A220027 A072489 A072487

Adjacent sequences:  A104347 A104348 A104349 * A104351 A104352 A104353

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Mar 06 2005

EXTENSIONS

More terms from David Wasserman, Apr 24 2008

STATUS

approved

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Last modified December 11 21:15 EST 2017. Contains 295919 sequences.