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%I #6 Jan 05 2020 11:26:40
%S 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 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 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 a(n) is the least prime P such that log(P)/log(p) >= valuation(n,p) for all primes p.
%C 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 S. 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. (DOI: 10.1112/plms/s2_14.1.347, a variant of better quality with an additional footnote is available at http://ramanujan.sirinudi.org/Volumes/published/ram15.html)
%o (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 Cf. A002182, A199337, A329571.
%K nonn
%O 1,1
%A _M. F. Hasler_, Jan 03 2020
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