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A100762 Let n = 2^e_2 * 3^e_3 * 5^e_5 * ... be the prime factorization of n and let P(n) = A100549(n); then a(n) = Product_{ q <= P(n) } q^e_q; a(1) = 1 by convention. 8

%I

%S 1,2,1,4,1,2,1,8,9,2,1,12,1,2,1,16,1,18,1,4,1,2,1,24,1,2,27,4,1,2,1,

%T 32,1,2,1,36,1,2,1,8,1,2,1,4,9,2,1,48,1,2,1,4,1,54,1,8,1,2,1,12,1,2,9,

%U 64,1,2,1,4,1,2,1,72,1,2,3,4,1,2,1,80,81,2,1,12,1,2,1,8,1,18,1,4,1,2,1,96,1

%N Let n = 2^e_2 * 3^e_3 * 5^e_5 * ... be the prime factorization of n and let P(n) = A100549(n); then a(n) = Product_{ q <= P(n) } q^e_q; a(1) = 1 by convention.

%H Antti Karttunen, <a href="/A100762/b100762.txt">Table of n, a(n) for n = 1..16384</a>

%H Antti Karttunen, <a href="/A100762/a100762.txt">Data supplement: n, a(n) computed for n = 1..100000</a>

%p # First load the procedure pp from A100549

%p # B = prod_{p <= pp(n)} p^e_p

%p B := proc(n) local v,f,pv; global pp; option remember;

%p pv := pp(n);

%p v := 1:

%p for f in op(2..-1,ifactors(n)) while f[1] <= pv do

%p v := v * f[1]^f[2];

%p end do;

%p return v;

%p end proc;

%t {1}~Join~Array[Function[{q, P}, Times @@ Power @@@ Select[q, First@# <= P &]] @@ {#, Prime@ PrimePi[1 + Max@ #[[All, -1]] ]} &@ FactorInteger[#] &, 96, 2] (* _Michael De Vlieger_, Nov 13 2018 *)

%o (PARI)

%o A100549(n) = if(1==n,1,prime(primepi(1+vecmax(factor(n)[,2]))));

%o A100762(n) = if(1==n,1,my(u = A100549(n), f=factor(n)); prod(i=1, #f~, if(f[i, 1]<=u, f[i, 1]^f[i, 2], 1))); \\ _Antti Karttunen_, Nov 11 2018

%Y Cf. A100549, A100417, A141586, A082725.

%K nonn

%O 1,2

%A _David Applegate_ and _N. J. A. Sloane_, Sep 15 2008

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Last modified June 13 00:57 EDT 2021. Contains 344980 sequences. (Running on oeis4.)