A377774 a(n) = largest prime p < gpf(n) that does not divide n, or p = nextprime(gpf(n)) for n in A055932, where gpf = A006530.

2, 3, 2, 3, 3, 5, 5, 3, 2, 3, 7, 5, 11, 5, 2, 3, 13, 5, 17, 3, 5, 7, 19, 5, 3, 11, 2, 5, 23, 7, 29, 3, 7, 13, 3, 5, 31, 17, 11, 3, 37, 5, 41, 7, 2, 19, 43, 5, 5, 3, 13, 11, 47, 5, 7, 5, 17, 23, 53, 7, 59, 29, 5, 3, 11, 7, 61, 13, 19, 3, 67, 5, 71, 31, 2, 17, 5

Offset: 1

Author

Michael De Vlieger, Nov 22 2024

Keywords

• nonn
• easy

Examples

			Let rad = A007947 and let P = A002110.
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.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002110, A006530, A007947, A053669, A055932, A079068.

Programs

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}]

Formula

a(n) = prime(i+1) for n in A002110.

a(p) = prevprime(p) for odd prime p.