A096432 Let n = 2^e_2 * 3^e_3 * 5^e_5 * ... be the prime factorization of n; sequence gives n such that 1 + max{e_2, e_3, ...} is a prime.

2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 26, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 55, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83

Offset: 1

Author

N. J. A. Sloane, Sep 18 2008

Keywords

• nonn

Comments

The old entry with this sequence number was a duplicate of A004555.

Sequence is of positive density. - Charles R Greathouse IV, Dec 07 2012

The asymptotic density of this sequence is Sum_{p prime} (1/zeta(p) - 1/zeta(p-1)) = 0.8817562193... - Amiram Eldar, Oct 18 2020

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..881 from R. J. Mathar)

Crossrefs

Cf. A060476, A074661.

Programs

Maple

(Maple code for this entry and A074661)
M:=2000; ans1:=[]; ans2:=[];
for n from 1 to M do
t1:=op(2..-1, ifactors(n)); t2:=nops(t1);
m1:=0; for i from 1 to t2 do m1:=max(m1,t1[i][2]); od:
if isprime(1+m1) then ans1:=[op(ans1),n]; fi;
if isprime(m1) then ans2:=[op(ans2),n]; fi;
od:

Mathematica

Select[Range[2, 100], PrimeQ[1 + Max[FactorInteger[#][[;; , 2]]]] &] (* Amiram Eldar, Oct 18 2020 *)

PARI

isA096432(n) = if(n<2,0,isprime(vecmax(factor(n)[,2])+1))