This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A340346 #20 Feb 25 2021 16:57:07
%S A340346 1,2,1,4,1,6,1,8,1,2,1,12,1,2,1,16,1,18,1,4,1,2,1,24,1,2,1,4,1,30,1,
%T A340346 32,1,2,1,36,1,2,1,8,1,6,1,4,1,2,1,48,1,2,1,4,1,54,1,8,1,2,1,60,1,2,1,
%U A340346 64,1,6,1,4,1,2,1,72,1,2,1,4,1,6,1,16,1,2,1,12
%N A340346 The largest divisor of n that is a term of A055932 (numbers divisible by all primes smaller than their largest prime factor).
%H A340346 Antti Karttunen, <a href="/A340346/b340346.txt">Table of n, a(n) for n = 1..8191</a>
%H A340346 Antti Karttunen, <a href="/A340346/a340346.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%H A340346 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A340346 For n >= 1, a(2n-1) = 1, a(2n) = A006519(2n) * A003961(a(A064989(2n))).
%F A340346 For n >= 1, lcm(A006519(n), A234959(n)) | a(n).
%e A340346 For n=2: the largest divisor of 2 is 2, and 2 qualifies as divisible by all primes smaller than its largest prime factor, 2 (since there are no smaller primes). So a(2) = 2.
%e A340346 For n=42: of 42's divisors, no multiples of 7 qualify as being divisible by all primes smaller than their largest prime factor (since that factor is 7 and no divisor of 42 is divisible by 5, a smaller prime). The largest of 42's other divisors is 6, which qualifies (since it is divisible by 2, the only prime smaller than 6's largest prime factor, 3). So a(42) = 6.
%t A340346 a[_?OddQ] = 1; a[n_] := Module[{f = FactorInteger[n]}, ind = Position[PrimePi /@ First /@ f - Range @ Length[f], _?(# > 0 &)]; If[ind == {}, n, Times @@ Power @@@ f[[1 ;; ind[[1, 1]] - 1]]]]; Array[a, 100] (* _Amiram Eldar_, Jan 14 2021 *)
%o A340346 (PARI) is(n) = my(f=factor(n)[, 1]~); f==primes(#f); \\ A055932
%o A340346 a(n) = vecmax(select(is, divisors(n))); \\ _Michel Marcus_, Jan 19 2021
%o A340346 (PARI)
%o A340346 A341629(n) = if(1==n,1,my(f=factor(n)[, 1]~); (primepi(f[#f])==#f));
%o A340346 A340346(n) = fordiv(n,d,if(A341629(n/d),return(n/d))); \\ _Antti Karttunen_, Feb 25 2021
%Y A340346 A003961, A006519, A055932, A064989, A341629 are used in a definition of this sequence.
%Y A340346 Sequences with related definitions: A327832, A328479.
%Y A340346 Cf. A234959.
%K A340346 nonn,easy
%O A340346 1,2
%A A340346 _Peter Munn_, Jan 04 2021