A329570 a(n) is the least prime P such that log(P)/log(p) >= valuation(n,p) for all primes p.

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, 7, 29, 5, 31, 37, 11, 17, 7, 11, 37, 19, 13, 11, 41, 7, 43, 11, 11, 23, 47, 17, 53, 29, 17, 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

Offset

1,1

Comments

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.

Links

Table of n, a(n) for n=1..77.

S. Ramanujan, Highly composite numbers, 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)

Prog

(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])

Crossrefs

Cf. A002182, A199337, A329571.

Sequence in context: A330404 A340575 A139171 * A279724 A050174 A115126

Adjacent sequences: A329567 A329568 A329569 * A329571 A329572 A329573

Keyword

nonn

Author

M. F. Hasler, Jan 03 2020

Status

approved