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 A212181 Largest odd divisor of tau(n): a(n) = A000265(A000005(n)). 4
 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 FORMULA a(n) = A000265(A000005(n)). 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, A000265, A212172. Sequence in context: A061893 A078530 A291568 * A256452 A010276 A214268 Adjacent sequences:  A212178 A212179 A212180 * A212182 A212183 A212184 KEYWORD nonn,mult,changed AUTHOR Matthew Vandermast, Jun 04 2012 STATUS approved

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Last modified December 8 12:26 EST 2019. Contains 329862 sequences. (Running on oeis4.)