

A329571


a(n) = Product_{prime p} p^floor(log_p P) with P = A329570(n) the least prime with log_p P >= valuation(n,p) for all primes p.


4



2, 2, 6, 60, 60, 6, 420, 27720, 27720, 60, 27720, 60, 360360, 420, 60, 12252240, 12252240, 27720, 232792560, 60, 420, 27720, 5354228880, 27720, 2329089562800, 360360, 2329089562800, 420, 2329089562800, 60, 72201776446800, 5342931457063200, 27720, 12252240, 420, 27720, 5342931457063200, 232792560, 360360, 27720, 219060189739591200, 420, 9419588158802421600, 27720
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OFFSET

1,1


COMMENTS

Related to the inequality (54) in Ramanujan's paper about highly composite numbers (HCN) A002182, also used in A199337: This is the square root of the (not minimal) bound a(n)^2 above which all HCN are divisible by n, according to the right part of that inequality.
Like the highly composite numbers A002182, all terms in this sequence are a product of primorials.


LINKS

Table of n, a(n) for n=1..44.
S. Ramanujan, Highly composite numbers, Proceedings of the London Mathematical Society ser. 2, vol. XIV, no. 1 (1915), pp 347409. (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)


FORMULA

a(n) = lcm([1..P]) = A003418(P) = A056604(i) with P = A329570(n), i = A000720(P).


PROG

(PARI) apply( {A329571(n)=vecprod([p^logint(n, p)p<primes([2, n=A329570(n)])])}, [1..44])


CROSSREFS

Cf. A329570, A002182 (highly composite numbers), A199337 (number of HCN not divisible by n), A003418 (lcm(1..n)), A056604 (lcm(1..prime(n)), A025487.
Sequence in context: A174589 A326942 A247943 * A270358 A156529 A184712
Adjacent sequences: A329567 A329569 A329570 * A329572 A329573 A329574


KEYWORD

nonn


AUTHOR

M. F. Hasler, Jan 03 2020


STATUS

approved



