cp's OEIS Frontend

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.

%I A100762 #15 Dec 01 2018 09:24:44
%S A100762 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 A100762 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 A100762 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 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.
%H A100762 Antti Karttunen, <a href="/A100762/b100762.txt">Table of n, a(n) for n = 1..16384</a>
%H A100762 Antti Karttunen, <a href="/A100762/a100762.txt">Data supplement: n, a(n) computed for n = 1..100000</a>
%p A100762 # First load the procedure pp from A100549
%p A100762 # B = prod_{p <= pp(n)} p^e_p
%p A100762 B := proc(n) local v,f,pv; global pp; option remember;
%p A100762 pv := pp(n);
%p A100762 v := 1:
%p A100762 for f in op(2..-1,ifactors(n)) while f[1] <= pv do
%p A100762 v := v * f[1]^f[2];
%p A100762 end do;
%p A100762 return v;
%p A100762 end proc;
%t A100762 {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 A100762 (PARI)
%o A100762 A100549(n) = if(1==n,1,prime(primepi(1+vecmax(factor(n)[,2]))));
%o A100762 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 A100762 Cf. A100549, A100417, A141586, A082725.
%K A100762 nonn
%O A100762 1,2
%A A100762 _David Applegate_ and _N. J. A. Sloane_, Sep 15 2008