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A212181 Largest odd divisor of tau(n): a(n) = A000265(A000005(n)). 5
1, 1, 1, 3, 1, 1, 1, 1, 3, 1, 1, 3, 1, 1, 1, 5, 1, 3, 1, 3, 1, 1, 1, 1, 3, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 1, 3, 3, 1, 1, 5, 3, 3, 1, 3, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 3, 7, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 3, 3, 1, 1, 1, 5, 5, 1, 1, 3, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Completely determined by the exponents >=2 in the prime factorization of n (cf. A212172).

Not the same as the number of odd divisors of n (A001227(n)); see example.

Multiplicative because A000005 is multiplicative and A000265 is completely multiplicative. - Andrew Howroyd, Aug 01 2018

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000

Index entries for sequences computed from exponents in factorization of n

FORMULA

a(n) = A000265(A000005(n)).

From Antti Karttunen, Jan 14 2020: (Start)

a(n) = A000005(n) / A000079(A295664(n)).

a(A108951(n)) = A331286(n).

(End)

EXAMPLE

48 has a total of 10 divisors (1, 2, 3, 4, 6, 8, 12, 16, 24 and 48). Since the largest odd divisor of 10 is 5, a(48) = 5.

MATHEMATICA

Table[Block[{nd=DivisorSigma[0, n]}, nd/2^IntegerExponent[nd, 2]], {n, 100}] (* Indranil Ghosh, Jul 19 2017, after PARI code *)

PROG

(PARI) a(n) = my(nd = numdiv(n)); nd/2^valuation(nd, 2); \\ Michel Marcus, Jul 19 2017

(Python)

from sympy import divisor_count, divisors

def a(n): return [i for i in divisors(divisor_count(n)) if i%2==1][-1]

print map(a, range(1, 101)) # Indranil Ghosh, Jul 19 2017

CROSSREFS

Cf. A000005, A000079, A000265, A108951, A212172, A295664, A331286 (applied to primorial inflation of n).

Sequence in context: A061893 A078530 A291568 * A256452 A330827 A010276

Adjacent sequences:  A212178 A212179 A212180 * A212182 A212183 A212184

KEYWORD

nonn,mult

AUTHOR

Matthew Vandermast, Jun 04 2012

STATUS

approved

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Last modified August 10 02:28 EDT 2020. Contains 336367 sequences. (Running on oeis4.)