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 A329570 #14 Jan 17 2025 07:22:16
%S A329570 2,2,3,5,5,3,7,11,11,5,11,5,13,7,5,17,17,11,19,5,7,11,23,11,29,13,29,
%T A329570 7,29,5,31,37,11,17,7,11,37,19,13,11,41,7,43,11,11,23,47,17,53,29,17,
%U A329570 13,53,29,11,11,19,29,59,5,61,31,11,67,13,11,67,17,23,7,71,11,73,37,29,19,11
%N A329570 a(n) is the least prime P such that log(P)/log(p) >= valuation(n,p) for all primes p.
%C A329570 Related to the inequality (54) in Ramanujan's paper about highly composite numbers A002182, also used in A199337: This is the largest prime factor of the bound A329571(n)^2 above which all highly composite numbers are divisible by n.
%H A329570 Amiram Eldar, <a href="/A329570/b329570.txt">Table of n, a(n) for n = 1..10000</a>
%H A329570 Srinivasa Ramanujan, <a href="https://doi.org/10.1112/plms/s2_14.1.347">Highly composite numbers</a>, Proceedings of the London Mathematical Society, Ser. 2, Vol. XIV, No. 1 (1915): 347-409. A variant of better quality with an additional footnote is available at <a href="http://ramanujan.sirinudi.org/Volumes/published/ram15.html">Ramanujan Papers</a>.
%F A329570 a(n) = A007918(A034699(n)). - _Amiram Eldar_, Jan 17 2025
%t A329570 a[n_] := NextPrime[Max[Power @@@ FactorInteger[n]] - 1]; a[1] = 2; Array[a, 100] (* _Amiram Eldar_, Jan 17 2025 *)
%o A329570 (PARI) apply( {A329570(n,f=Col(factor(max(n,2))), P=nextprime(vecmax([log(f[1])*f[2] | f<-f])))=[while( logint(P,f[1]) < f[2], P=nextprime(P+1)) | f<-f]; P}, [1..99])
%Y A329570 Cf. A002182, A007918, A034699, A199337, A329571.
%K A329570 nonn
%O A329570 1,1
%A A329570 _M. F. Hasler_, Jan 03 2020