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A253139 a(n) = lcm_{d|n} tau(d), where tau(d) represents the number of divisors of d (A000005(d)). 11
1, 2, 2, 6, 2, 4, 2, 12, 6, 4, 2, 12, 2, 4, 4, 60, 2, 12, 2, 12, 4, 4, 2, 24, 6, 4, 12, 12, 2, 8, 2, 60, 4, 4, 4, 36, 2, 4, 4, 24, 2, 8, 2, 12, 12, 4, 2, 120, 6, 12, 4, 12, 2, 24, 4, 24, 4, 4, 2, 24, 2, 4, 12, 420, 4, 8, 2, 12, 4, 8, 2, 72, 2, 4, 12, 12, 4, 8 (list; graph; refs; listen; history; text; internal format)
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

If n = Product_ prime(i)^e(i), then a(n) = Product_ A003418(e(i)+1).

a(n) = Product_{d|n} A253141(d).

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 *)

PROG

(PARI) a(n) = my(d = divisors(n)); lcm(vector(#d, k, numdiv(d[k]))); \\ Michel Marcus, Jan 23 2015

CROSSREFS

A250270 gives range of values. A141586 lists numbers n such that a(n) divides n.

Cf. A003418, A253141.

Sequence in context: A278234 A068976 A265392 * A318519 A317848 A124859

Adjacent sequences:  A253136 A253137 A253138 * A253140 A253141 A253142

KEYWORD

nonn,easy,mult

AUTHOR

Matthew Vandermast, Dec 27 2014

STATUS

approved

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Last modified April 20 14:27 EDT 2019. Contains 322310 sequences. (Running on oeis4.)