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A072411 LCM of exponents in prime factorization of n, a(1) = 1. 27
1, 1, 1, 2, 1, 1, 1, 3, 2, 1, 1, 2, 1, 1, 1, 4, 1, 2, 1, 2, 1, 1, 1, 3, 2, 1, 3, 2, 1, 1, 1, 5, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 2, 2, 1, 1, 4, 2, 2, 1, 2, 1, 3, 1, 3, 1, 1, 1, 2, 1, 1, 2, 6, 1, 1, 1, 2, 1, 1, 1, 6, 1, 1, 2, 2, 1, 1, 1, 4, 4, 1, 1, 2, 1, 1, 1, 3, 1, 2, 1, 2, 1, 1, 1, 5, 1, 2, 2, 2, 1, 1, 1, 3, 1, 1, 1, 6, 1, 1, 1, 4, 1, 1, 1, 2, 2, 1, 1, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10080

Index entries for sequences computed from exponents in factorization of n

Index entries for sequences related to lcm's

FORMULA

a(1) = 1; for n > 1, a(n) = lcm(A067029(n), a(A028234(n)). - Antti Karttunen, Aug 09 2016

From Antti Karttunen, Aug 22 2017: (Start)

a(n) = A284569(A156552(n)).

a(n) = A290103(A181819(n)).

a(A289625(n)) = A002322(n).

a(A290095(n)) = A055092(n).

a(A275725(n)) = A060131(n).

a(A260443(n)) = A277326(n).

a(A283477(n)) = A284002(n). (End)

EXAMPLE

n = 288 = 2*2*2*2*2*3*3; lcm(5,2) = 10; Product(5,2) = 10, max(5,2) = 5;

n = 180 = 2*2*3*3*5; lcm(2,2,1) = 2; Product(2,2,1) = 4; max(2,2,1) = 2; it deviates both from maximum of exponents (A051903, for the first time at n=72), and product of exponents (A005361, for the first time at n=36).

For n = 36 = 2*2*3*3 = 2^2 * 3^2 we have a(36) = lcm(2,2) = 2.

For n = 72 = 2*2*2*3*3 = 2^3 * 3^2 we have a(72) = lcm(2,3) = 6.

For n = 144 = 2^4 * 3^2 we have a(144) = lcm(2,4) = 4.

For n = 360 = 2^3 * 3^2 * 5^1 we have a(360) = lcm(1,2,3) = 6.

MATHEMATICA

Table[LCM @@ Last /@ FactorInteger[n], {n, 2, 100}] (* Ray Chandler, Jan 24 2006 *)

PROG

(Scheme, with memoization-macro definec)

(definec (A072411 n) (if (= 1 n) 1 (lcm (A067029 n) (A072411 (A028234 n))))) ;; Antti Karttunen, Aug 09 2016

(Python)

from sympy import lcm, factorint

def a(n):

....l=[]

....f=factorint(n)

....for i in f: l+=[f[i], ]

....return lcm(l)

print [a(n) for n in xrange(1, 151)] # Indranil Ghosh, Mar 25 2017

(PARI) a(n) = lcm(factor(n)[, 2]); \\ Michel Marcus, Mar 25 2017

CROSSREFS

Cf. A028234, A067029, A072412-A072414, A273058, A284569, A290103.

Similar sequences: A001222 (sum of exponents), A005361 (product), A051903 (maximal exponent), A051904 (minimal exponent), A052409 (gcd of exponents), A267115 (bitwise-and), A267116 (bitwise-or), A268387 (bitwise-xor).

Cf. also A055092, A060131.

Differs from A290107 for the first time at n=144.

After the initial term, differs from A157754 for the first time at n=360.

Sequence in context: A051903 A324912 A157754 * A290107 A212180 A091050

Adjacent sequences:  A072408 A072409 A072410 * A072412 A072413 A072414

KEYWORD

nonn

AUTHOR

Labos Elemer, Jun 17 2002

EXTENSIONS

a(1) = 1 prepended and the data section filled up to 120 terms by Antti Karttunen, Aug 09 2016

STATUS

approved

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Last modified October 15 22:25 EDT 2019. Contains 328038 sequences. (Running on oeis4.)