A161506 - OEIS

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A161506

Number of divisors of n that are greater than phi(n)/2, where phi is Euler's totient function.

1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 4, 1, 2, 2, 2, 1, 3, 1, 3, 2, 2, 1, 4, 1, 2, 1, 3, 1, 5, 1, 2, 2, 2, 1, 4, 1, 2, 2, 3, 1, 4, 1, 3, 2, 2, 1, 4, 1, 2, 2, 3, 1, 3, 1, 3, 2, 2, 1, 6, 1, 2, 2, 2, 1, 4, 1, 3, 2, 3, 1, 4, 1, 2, 2, 3, 1, 4, 1, 3, 1, 2, 1, 5, 1, 2, 2, 3, 1, 5, 1, 3, 2, 2, 1, 4, 1, 2, 2, 3, 1, 4, 1, 3, 2 (list; graph; refs; listen; history; internal format)

	OFFSET	`1,2`
	COMMENTS	`When computing the cyclotomic polynomial Phi(n,x) as the quotient of sparse polynomials (see Arnold and Monagan), the divisors of n greater than phi(n)/2 are not required because only powers up to phi(n)/2 need to be computed; the remaining terms can be inferred because all cyclotomic polynomials are palindromic for n>1. This sequence grows slowly; k first occurs at A161507(k).`
	LINKS	`Andrew Arnold and Michael Monagan Calculating cyclotomic polynomials of very large height`
	MATHEMATICA	`Table[d=Divisors[n]; e=EulerPhi[n]; Length[Select[d, #>e/2&]], {n, 100}]`
	CROSSREFS	`Sequence in context: A055874 A195155 A178544 * A066451 A091090 A066075` `Adjacent sequences: A161503 A161504 A161505 * A161507 A161508 A161509`
	KEYWORD	`nonn`
	AUTHOR	`T. D. Noe (noe(AT)sspectra.com), Jun 17 2009`

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Last modified February 15 23:53 EST 2012. Contains 205860 sequences.