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.

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, 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, 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

Offset: 1

Author

David Applegate and N. J. A. Sloane, Sep 15 2008

Keywords

• nonn

Examples

			If n = 8 = 2^3, a(n) = (largest prime <= 3+1) = 3.
If n = 480 = 2^5*3*5, a(n) = (largest prime <= 1 + max{5,1,1}) = 5.
		

Links

• David Applegate and N. J. A. Sloane, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A100762, A100417, A141586, A082725.

Programs

Maple

# if n = prod_p p^e_p, then
# pp = largest prime <= 1 + max e_p
with(numtheory):
pp := proc(n) local f,m; option remember;
if (n = 1) then
return 1;
end if;
m := 1:
for f in op(2..-1,ifactors(n)) do
if (f[2] > m) then
m := f[2]:
end if;
end do;
prevprime(m+2);
end proc;

Mathematica

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

PARI

a(n) = if (n==1, 1, precprime(1 + vecmax(factor(n)[,2]~))); \\ Michel Marcus, Nov 14 2018