OFFSET
1,2
COMMENTS
A version of A336957 defined just on the odd numbers.
Let Ker(k), the kernel of k, denote the set of primes dividing k. Thus Ker(36) = {2,3}, Ker(1) = {}. Then Product_{p in Ker(k)} p = A000265(k), which is denoted by ker(k).
Theorem 1: For n>2, a(n) is the smallest odd number m not yet in the sequence such that
(i) Ker(m) intersect Ker(a(n-1)) is nonempty,
(ii) Ker(m) intersect Ker(a(n-2)) is empty, and
(iii) The set Ker(m) \ Ker(a(n-1)) is nonempty.
LINKS
N. J. A. Sloane, Table of n, a(n) for n = 1..10000
MAPLE
with(numtheory);
N:= 10^3: # to get a(1) to a(n) where a(n+1) is the first term > N
B:= Vector(N, datatype=integer[1]):
A[1]:=1; A[2]:=3;
for n from 3 do
for k from 5 to N by 2 do
if B[k] = 0 and igcd(k, A[n-1]) > 1 and igcd(k, A[n-2]) = 1 then
if nops(factorset(k) minus factorset(A[n-1])) > 0 then
A[n]:= k;
B[k]:= 1;
break;
fi;
fi;
od:
if k > N then break; fi;
od:
s1:=[seq(A[i], i=1..n-1)];
PROG
(PARI) a338351(upto)={my(v=[1, 3]); for(n=1, upto, forstep(k=5, oo, 2, if(!vecsearch(vecsort(v), k), if(gcd(k, v[#v])>1&&gcd(k, v[#v-1])==1, if(#setminus(Set(factor(k)[, 1]), Set(factor(v[#v])[, 1]))>0, v=concat(v, [k]); break))))); v};
a338351(60) \\ Hugo Pfoertner, Oct 30 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Oct 30 2020
STATUS
approved