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 A161506 Number of divisors of n that are greater than phi(n)/2, where phi is Euler's totient function. 2
 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; text; 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 Antti Karttunen, Table of n, a(n) for n = 1..65537 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}] PROG (PARI) A161506(n) = { my(p2 = eulerphi(n)); sumdiv(n, d, ((2*d)>p2)); }; \\ Antti Karttunen, Jan 19 2020 CROSSREFS Cf. A000005, A000010. Sequence in context: A055874 A195155 A178544 * A066451 A328048 A363522 Adjacent sequences: A161503 A161504 A161505 * A161507 A161508 A161509 KEYWORD nonn AUTHOR T. D. Noe, Jun 17 2009 STATUS approved

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Last modified December 7 18:04 EST 2023. Contains 367660 sequences. (Running on oeis4.)