OFFSET
1,2
COMMENTS
A divisibility sequence (cf. Ward link and second formula).
a(n) depends only on prime signature of n (cf. A025487). So a(24) = a(375) since 24 = 2^3*3 and 375 = 3*5^3 both have prime signature (3,1).
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..10000
Morgan Ward, A note on divisibility sequences, Bull. Amer. Math. Soc., 45 (1939), 334-336.
FORMULA
EXAMPLE
The divisors of 20 are 1, 2, 4, 5, 10 and 20, which have 1, 2, 3, 2, 4 and 6 divisors respectively. The least common multiple of 1, 2, 3, 2, 4 and 6 is 12; therefore, a(20) = 12.
MATHEMATICA
Table[LCM@@DivisorSigma[0, Divisors[n]], {n, 100}] (* Harvey P. Dale, Sep 01 2017 *)
lcm[n_] := lcm[n] = LCM @@ Range[n]; a[1] = 1; a[n_] := Times @@ (lcm [Last[#] + 1] & /@ FactorInteger[n]); Array[a, 100] (* Amiram Eldar, Sep 11 2020 *)
PROG
(PARI) a(n) = my(d = divisors(n)); lcm(vector(#d, k, numdiv(d[k]))); \\ Michel Marcus, Jan 23 2015
CROSSREFS
KEYWORD
nonn,easy,mult
AUTHOR
Matthew Vandermast, Dec 27 2014
STATUS
approved