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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.

%I A377774 #14 Nov 24 2024 09:38:36
%S A377774 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,
%T A377774 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,
%U A377774 53,7,59,29,5,3,11,7,61,13,19,3,67,5,71,31,2,17,5
%N 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.
%H A377774 Michael De Vlieger, <a href="/A377774/b377774.txt">Table of n, a(n) for n = 1..10000</a>
%F A377774 a(n) = prime(i+1) for n in A002110.
%F A377774 a(p) = prevprime(p) for odd prime p.
%e A377774 Let rad = A007947 and let P = A002110.
%e A377774 a(1) = 2 since P(0) = 1.
%e A377774 a(2) = 3 since P(1) = 2.
%e A377774 a(3) = 2 since prevprime(gpf(3)) = 2.
%e A377774 a(4) = 3 since rad(4) = 2 = P(1).
%e A377774 a(6) = 5 since P(2) = 6.
%e A377774 a(9) = 2 since gpf(9) = 3.
%e A377774 a(10) = 3 since 10 = 2*5.
%e A377774 a(12) = 5 since rad(12) = 6 = P(2).
%e A377774 a(14) = 5 since 14 = 2*7.
%e A377774 a(15) = 2 since 15 = 3*5, etc.
%t A377774 Table[If[
%t A377774   Or[IntegerQ@ Log2[n],
%t A377774     And[EvenQ[n], Union@ Differences@ PrimePi[#] == {1}] ],
%t A377774   NextPrime[#[[-1]] ],
%t A377774   q = NextPrime[#[[-1]], -1];
%t A377774     While[Divisible[n, q], q = NextPrime[q, -1]]; q] &[
%t A377774   FactorInteger[n][[All, 1]] ], {n, 120}]
%Y A377774 Cf. A002110, A006530, A007947, A053669, A055932, A079068.
%K A377774 nonn,easy
%O A377774 1,1
%A A377774 _Michael De Vlieger_, Nov 22 2024