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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
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
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
Sequence in context: A055874 A195155 A178544 * A066451 A328048 A363522
KEYWORD
nonn
AUTHOR
T. D. Noe, Jun 17 2009
STATUS
approved