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A100549 Let n = 2^e_2 * 3^e_ * 5^e_ * ... be the prime factorization of n; then a(n) = largest prime <= 1 + max{e_2, e_3, e_5, ...}; a(1) = 1 by convention. 6

%I

%S 1,2,2,3,2,2,2,3,3,2,2,3,2,2,2,5,2,3,2,3,2,2,2,3,3,2,3,3,2,2,2,5,2,2,

%T 2,3,2,2,2,3,2,2,2,3,3,2,2,5,3,3,2,3,2,3,2,3,2,2,2,3,2,2,3,7,2,2,2,3,

%U 2,2,2,3,2,2,3,3,2,2,2,5,5,2,2,3,2,2,2,3,2,3,2,3,2,2,2,5,2,3,3,3,2,2,2,3,2

%N Let n = 2^e_2 * 3^e_ * 5^e_ * ... be the prime factorization of n; then a(n) = largest prime <= 1 + max{e_2, e_3, e_5, ...}; a(1) = 1 by convention.

%H David Applegate and N. J. A. Sloane, <a href="/A100549/b100549.txt">Table of n, a(n) for n = 1..10000</a>

%e If n = 8 = 2^3, a(n) = (largest prime <= 3+1) = 3.

%e If n = 480 = 2^5*3*5, a(n) = (largest prime <= 1 + max{5,1,1}) = 5.

%p # if n = prod_p p^e_p, then

%p # pp = largest prime <= 1 + max e_p

%p with(numtheory):

%p pp := proc(n) local f,m; option remember;

%p if (n = 1) then

%p return 1;

%p end if;

%p m := 1:

%p for f in op(2..-1,ifactors(n)) do

%p if (f[2] > m) then

%p m := f[2]:

%p end if;

%p end do;

%p prevprime(m+2);

%p end proc;

%t {1}~Join~Array[Prime@PrimePi[1 + Max@FactorInteger[#][[All, -1]]] &, 105, 2] (* _Michael De Vlieger_, Nov 13 2018 *)

%o (PARI) a(n) = if (n==1, 1, precprime(1 + vecmax(factor(n)[,2]~))); \\ _Michel Marcus_, Nov 14 2018

%Y Cf. A100762, 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 July 24 20:26 EDT 2021. Contains 346273 sequences. (Running on oeis4.)