A100549 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

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

EXAMPLE

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.

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 *)

PROG

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

CROSSREFS

Cf. A100762, A100417, A141586, A082725.

Sequence in context: A082091 A375431 A334216 * A085962 A160821 A300225

Adjacent sequences: A100546 A100547 A100548 * A100550 A100551 A100552

KEYWORD

nonn

AUTHOR

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

STATUS

approved