A369690 a(n) = max(A119288(n), A053669(n)).
2, 3, 2, 3, 2, 5, 2, 3, 2, 5, 2, 5, 2, 7, 5, 3, 2, 5, 2, 5, 7, 11, 2, 5, 2, 13, 2, 7, 2, 7, 2, 3, 11, 17, 7, 5, 2, 19, 13, 5, 2, 5, 2, 11, 5, 23, 2, 5, 2, 5, 17, 13, 2, 5, 11, 7, 19, 29, 2, 7, 2, 31, 7, 3, 13, 5, 2, 17, 23, 5, 2, 5, 2, 37, 5, 19, 11, 5, 2, 5, 2
Offset: 1
Examples
Let p be the second least prime factor of n or 1 if n is a prime power, and let q be the smallest prime that does not divide n.
a(1) = 2 since max(p, q) = max(1, 2) = 2.
a(2) = 3 since max(p, q) = max(1, 3) = 3.
a(4) = 3 since max(p, q) = max(1, 3) = 3.
a(6) = 5 since max(p, q) = max(3, 5) = 5.
a(9) = 2 since max(p, q) = max(1, 2) = 2.
a(15) = 5 since max(p, q) = max(5, 2) = 5.
a(36) = 5 since max(p, q) = max(3, 5) = 5.
Generally,
a(n) = 2 for n in A061345 = union of {1} and sequences { m*p : prime p > 2, rad(m) | p }.
a(n) = 3 for n in A000079 = { 2*m : rad(m) | 2 }.
a(n) = 5 for k in { k = m*d : rad(m) | d, d in {6, 10, 15} }.
a(n) = 7 for k in { k = m*d : rad(m) | d, d in {14, 21, 30, 35} }.
a(n) = 11 for k in { k = m*d : rad(m) | d, d in {22, 33, 55, 77, 210} }, etc.
Links
- Michael De Vlieger, Table of n, a(n) for n = 1..10000
Crossrefs
Programs
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Mathematica
{2}~Join~Array[If[PrimePowerQ[#], q = 2; While[Divisible[#, q], q = NextPrime[q]]; q, q = 2; While[Divisible[#, q], q = NextPrime[q]]; Max[FactorInteger[#][[2, 1]], q]] &, 120, 2]
Comments