OFFSET
1,3
COMMENTS
The "odd part" (largest odd divisor) of the number of divisors of n is a function of the exponents >=2 in the prime factorization of n (cf. A212172, A212181).
The number 1 appears a total of 18 times (see Graeme link for proof). Ramanujan proved that no number appears an infinite number of times (see Ramanujan link). It would be interesting to know more about a) which odd numbers appear in the sequence and b) how many times a number of a given size can appear in the sequence. See also A160233.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
A. Flammenkamp, List of the first 1200 highly composite numbers
Graeme McRae, Highly Composite Numbers
S. Ramanujan, Highly Composite Numbers (p. 34).
S. Ramanujan, Highly composite numbers, Proc. Lond. Math. Soc. 14 (1915), 347-409; reprinted in Collected Papers, Ed. G. H. Hardy et al., Cambridge 1927; Chelsea, NY, 1962.
EXAMPLE
CROSSREFS
KEYWORD
nonn
AUTHOR
Matthew Vandermast, Jun 08 2012
STATUS
approved