A290077 a(n) = A000010(A005940(1+n)).

1, 1, 2, 2, 4, 2, 6, 4, 6, 4, 8, 4, 20, 6, 18, 8, 10, 6, 12, 8, 24, 8, 24, 8, 42, 20, 40, 12, 100, 18, 54, 16, 12, 10, 20, 12, 40, 12, 36, 16, 60, 24, 48, 16, 120, 24, 72, 16, 110, 42, 84, 40, 168, 40, 120, 24, 294, 100, 200, 36, 500, 54, 162, 32, 16, 12, 24, 20, 48, 20, 60, 24, 72, 40, 80, 24, 200, 36, 108, 32, 120, 60, 120

Offset: 0

Author

Antti Karttunen, Jul 19 2017

Keywords

• nonn

Comments

Each n occurs A014197(n) times in total in this sequence.

Links

• Antti Karttunen, Table of n, a(n) for n = 0..16384
• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A000010, A000040, A005940, A014197, A290076, A323915, A324052, A324054, A364568.

Programs

Mathematica

f[n_, i_, x_]:=f[n, i, x]=Which[n==0, x, EvenQ[n], f[n/2, i + 1, x], f[(n - 1)/2, i, x Prime[i]]]; a005940[n_]:=f[n - 1, 1, 1]; Table[EulerPhi[a005940[n + 1]], {n, 0, 100}] (* Indranil Ghosh, Jul 20 2017 *)

PARI

A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };
A290077(n) = eulerphi(A005940(1+n));

PARI

A290077(n) = { my(p=2,z=1); while(n, if(!(n%2), p=nextprime(1+p), z *= (p-(1==(n%4)))); n>>=1); (z); }; \\ Antti Karttunen, Aug 05 2023

Sage

def A290077(n):
    i = 1
    m = 1
    while n > 0:
      if 0==(n%2):
        n = n//2
        i += 1
      else:
        if(1==(n%4)):
          n = (n-1)//4
          m *= sloane.A000040(i)-1
          i += 1
        else:
          n = (n-1)//2
          m *= sloane.A000040(i)
    return m

Scheme

(define (A290077 n) (A000010 (A005940 (+ 1 n))))

Scheme

(define (A290077 n) (let loop ((n n) (m 1) (i 1)) (cond ((zero? n) m) ((even? n) (loop (/ n 2) m (+ 1 i))) ((= 1 (modulo n 4)) (loop (/ (- n 1) 4) (* m (- (A000040 i) 1)) (+ 1 i))) (else (loop (/ (- n 1) 2) (* m (A000040 i)) i))))) ;; Requires only an implementation of A000040, see for example under A083221.

Formula

a(n) = A000010(A005940(1+n)).