A100371 - OEIS

A100371

a(n) = 2^phi(n) - 1 = A066781(n) - 1.

1, 1, 3, 3, 15, 3, 63, 15, 63, 15, 1023, 15, 4095, 63, 255, 255, 65535, 63, 262143, 255, 4095, 1023, 4194303, 255, 1048575, 4095, 262143, 4095, 268435455, 255, 1073741823, 65535, 1048575, 65535, 16777215, 4095, 68719476735, 262143, 16777215, 65535

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OFFSET

1,3

COMMENTS

Number of nonempty subsets of reduced residue system [RRS(n)] modulo n.

LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000

N. Bliss, B. Fulan, S. Lovett, and J. Sommars, Strong Divisibility, Cyclotomic Polynomials, and Iterated Polynomials, Amer. Math. Monthly, 120 (2013), 519-536.

FORMULA

a(n) = Sum_{i=1..n} binomial(phi(n), i). - Enrique Pérez Herrero, Mar 10 2012

MAPLE

A100371:=n->2^numtheory[phi](n)-1: seq(A100371(n), n=1..60); # Wesley Ivan Hurt, Apr 14 2017

MATHEMATICA

Table[2^EulerPhi[n] - 1, {n, 1, 50}]

PROG

(PARI) a(n) = 2^eulerphi(n) - 1; \\ Michel Marcus, Apr 14 2017

(Python)

from sympy import totient

def a(n): return 2**totient(n) - 1 # Indranil Ghosh, Apr 14 2017

CROSSREFS

Cf. A000010, A066781.

Sequence in context: A368117 A282009 A282485 * A286206 A286501 A287100

Adjacent sequences: A100368 A100369 A100370 * A100372 A100373 A100374

KEYWORD

easy,nonn

AUTHOR

Labos Elemer, Nov 30 2004

EXTENSIONS

Entry revised by N. J. A. Sloane, Jun 07 2013

STATUS

approved