OFFSET
1,1
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = prime(i+1) for n in A002110.
a(p) = prevprime(p) for odd prime p.
EXAMPLE
a(1) = 2 since P(0) = 1.
a(2) = 3 since P(1) = 2.
a(3) = 2 since prevprime(gpf(3)) = 2.
a(4) = 3 since rad(4) = 2 = P(1).
a(6) = 5 since P(2) = 6.
a(9) = 2 since gpf(9) = 3.
a(10) = 3 since 10 = 2*5.
a(12) = 5 since rad(12) = 6 = P(2).
a(14) = 5 since 14 = 2*7.
a(15) = 2 since 15 = 3*5, etc.
MATHEMATICA
Table[If[
Or[IntegerQ@ Log2[n],
And[EvenQ[n], Union@ Differences@ PrimePi[#] == {1}] ],
NextPrime[#[[-1]] ],
q = NextPrime[#[[-1]], -1];
While[Divisible[n, q], q = NextPrime[q, -1]]; q] &[
FactorInteger[n][[All, 1]] ], {n, 120}]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Michael De Vlieger, Nov 22 2024
STATUS
approved