|
|
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.
|
|
9
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
The old entry with this sequence number was a duplicate of A004555.
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
|
|
|
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 *)
|
|
PROG
|
(PARI) isA096432(n) = if(n<2, 0, isprime(vecmax(factor(n)[, 2])+1))
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|