A290076 -id:A290076 - cp's OEIS frontend

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

Antti Karttunen, Jul 19 2017

nonn

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

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

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

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 *)

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));

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

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

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

(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.

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

A290082 Restricted growth sequence transform of A289625(A003961(n)).

Original entry on oeis.org

1, 2, 3, 4, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 11, 14, 7, 15, 16, 17, 15, 11, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 23, 30, 31, 32, 33, 34, 20, 35, 36, 37, 30, 38, 39, 40, 41, 42, 19, 43, 44, 45, 37, 46, 47, 23, 48, 49, 50, 19, 51, 52, 43, 53, 54, 34, 55, 56, 57, 58, 59, 60, 61, 62, 30, 63, 64, 65, 66, 42, 67, 68, 34, 69, 30, 70, 71, 68, 72, 61

Offset: 1

Antti Karttunen, Jul 20 2017

nonn

For all i, j: a(i) = a(j) => A003972(i) = A003972(j).

Antti Karttunen, Table of n, a(n) for n = 1..16384

Cf. A003961, A003972, A289625, A290076.

rgs_transform(invec) = { my(occurrences = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(occurrences,invec[i]), my(pp = mapget(occurrences, invec[i])); outvec[i] = outvec[pp] , mapput(occurrences,invec[i],i); outvec[i] = u; u++ )); outvec; };
write_to_bfile(start_offset,vec,bfilename) = { for(n=1, length(vec), write(bfilename, (n+start_offset)-1, " ", vec[n])); }
A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); }; \\ This function from Michel Marcus
A289625(n) = { my(m=1,p=2,v=znstar(n)[2]); for(i=1,length(v),m *= p^v[i]; p = nextprime(p+1)); (m); };
write_to_bfile(1,rgs_transform(vector(16384,n,A289625(A003961(n)))),"b290082_upto16384.txt");

cp's OEIS Frontend

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

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A290082 Restricted growth sequence transform of A289625(A003961(n)).

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