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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.

%I A100549 #13 Nov 14 2018 02:39:56
%S A100549 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 A100549 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 A100549 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 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.
%H A100549 David Applegate and N. J. A. Sloane, <a href="/A100549/b100549.txt">Table of n, a(n) for n = 1..10000</a>
%e A100549 If n = 8 = 2^3, a(n) = (largest prime <= 3+1) = 3.
%e A100549 If n = 480 = 2^5*3*5, a(n) = (largest prime <= 1 + max{5,1,1}) = 5.
%p A100549 # if n = prod_p p^e_p, then
%p A100549 # pp = largest prime <= 1 + max e_p
%p A100549 with(numtheory):
%p A100549 pp := proc(n) local f,m; option remember;
%p A100549 if (n = 1) then
%p A100549 return 1;
%p A100549 end if;
%p A100549 m := 1:
%p A100549 for f in op(2..-1,ifactors(n)) do
%p A100549 if (f[2] > m) then
%p A100549 m := f[2]:
%p A100549 end if;
%p A100549 end do;
%p A100549 prevprime(m+2);
%p A100549 end proc;
%t A100549 {1}~Join~Array[Prime@PrimePi[1 + Max@FactorInteger[#][[All, -1]]] &, 105, 2] (* _Michael De Vlieger_, Nov 13 2018 *)
%o A100549 (PARI) a(n) = if (n==1, 1, precprime(1 + vecmax(factor(n)[,2]~))); \\ _Michel Marcus_, Nov 14 2018
%Y A100549 Cf. A100762, A100417, A141586, A082725.
%K A100549 nonn
%O A100549 1,2
%A A100549 _David Applegate_ and _N. J. A. Sloane_, Sep 15 2008