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a(n) = A000010(A005940(1+n)).
10

%I #32 Aug 06 2023 08:19:16

%S 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,

%T 100,18,54,16,12,10,20,12,40,12,36,16,60,24,48,16,120,24,72,16,110,42,

%U 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

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

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

%H Antti Karttunen, <a href="/A290077/b290077.txt">Table of n, a(n) for n = 0..16384</a>

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

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

%t 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 *)

%o (PARI)

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

%o A290077(n) = eulerphi(A005940(1+n));

%o (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

%o (Sage)

%o def A290077(n):

%o i = 1

%o m = 1

%o while n > 0:

%o if 0==(n%2):

%o n = n//2

%o i += 1

%o else:

%o if(1==(n%4)):

%o n = (n-1)//4

%o m *= sloane.A000040(i)-1

%o i += 1

%o else:

%o n = (n-1)//2

%o m *= sloane.A000040(i)

%o return m

%o (Scheme) (define (A290077 n) (A000010 (A005940 (+ 1 n))))

%o (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.

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

%K nonn

%O 0,3

%A _Antti Karttunen_, Jul 19 2017