A035532 a(n) = 2*phi(n) if n composite, or 2*phi(n) - (A000120(n)-1) if n prime, where phi = A000010, Euler's totient function, and a(1) = 1.

1, 2, 3, 4, 7, 4, 10, 8, 12, 8, 18, 8, 22, 12, 16, 16, 31, 12, 34, 16, 24, 20, 41, 16, 40, 24, 36, 24, 53, 16, 56, 32, 40, 32, 48, 24, 70, 36, 48, 32, 78, 24, 81, 40, 48, 44, 88, 32, 84, 40, 64, 48, 101, 36, 80, 48, 72, 56, 112, 32, 116, 60, 72, 64, 96, 40, 130, 64, 88, 48, 137

Offset: 1

Author

Daniele Parisse

Keywords

• nonn
• easy

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000010, A010051, A035531, A048881, A297111, A297115.

Programs

Haskell

a035532 1 = 1
a035532 n = if a010051' n == 0 then phi2 else phi2 - a000120 n + 1
            where phi2 = 2 * a000010 n
-- Reinhard Zumkeller, Feb 04 2015

Mathematica

Insert[Table[If[PrimeQ[n],2*EulerPhi[n] - DigitCount[n, 2][[1]] + 1, 2*EulerPhi[n]], {n, 2, 100}], 1, 1] (* Stefan Steinerberger, Apr 11 2006 *)

PARI

A035532(n)=2*eulerphi(n)-if(isprime(n),hammingweight(n)-1,n==1) \\ M. F. Hasler, Mar 10 2018

Formula

a(n) = 2*A000010(n) - A010051(n)*A048881(n-1), for n > 1. - Reinhard Zumkeller, Feb 04 2015, edited by M. F. Hasler, Mar 10 2018

For many values of n, the inverse Möbius transform of this sequence (g.f.: Sum a(n)*x^n/(1-x^n)) equals A005187, but this is not the case for composite n such that A297115(n) <> 0. The equality does hold for A297111 instead. - Antti Karttunen & M. F. Hasler, Mar 10 2018

Extensions

More terms from James Sellers

Definition amended for a(1) = 1 by M. F. Hasler, Mar 10 2018