A253563 -id:A253563 - cp's OEIS frontend

A252738 Row products of irregular table A005940: a(0) = 1; a(1) = 2; for n > 1: 2^(2^(n-2)) * a(n-1) * A003961(a(n-1)); also row products of A163511, A253563, A253565, and A332977.

1, 2, 12, 2160, 2449440000, 8488905214204800000000000, 3025568387202006082882734693673523654400000000000000000000000000

Offset: 0

Antti Karttunen, Dec 21 2014

nonn

			From _Michael De Vlieger_, Jul 21 2023: (Start)
a(0) = 1 = product of {1},
a(1) = 2^1 = product of {2},
a(2) = 2^2 * 3^1 = product of {3, 2^2},
a(3) = 2^4 * 3^3 * 5^1 = product of {5, 2^1*3^1, 3^2, 2^3},
a(4) = 2^8 * 3^7 * 5^4 * 7^1 = product of
  {7, 2^1*5^1, 3^1*5^1, 2^2*3^1, 5^2, 2^1*3^2, 3^3, 2^4},
...
Table of e(n,k) where a(n) = Product_{k=1..n+1} prime(k)^e(n,k):
prime(k)|    2    3    5   7  11  13  17  19 23 29 31 ...
   n\k  |    1    2    3   4   5   6   7   8  9 10 11 ...
   ----------------------------------------------------
    0   |    1
    1   |    2    1
    2   |    4    3    1
    3   |    8    7    4   1
    4   |   16   15   11   5   1
    5   |   32   31   26  16   6   1
    6   |   64   63   57  42  22   7   1
    7   |  128  127  120  99  64  29   8   1
    8   |  256  255  247 219 163  93  37   9  1
    9   |  512  511  502 466 382 256 130  46 10  1
   10   | 1024 1023 1013 968 848 638 386 176 56 11  1
  ... (End)

Alois P. Heinz, Table of n, a(n) for n = 0..9

These are row products of irregular tables A005940, A163511, A253563 and A253565, which all are shaped like a binary tree.
Partial products of A252740.
Cf. A252737 (row sums), A252739 (divided by n), A252741 (divided by n!).
Cf. A000079, A000225, A000290, A003961, A163511, A191555, A266639, A267096, A332977.

Table[Times @@ Array[Prime[# + 1]^Sum[Binomial[n, # + j], {j, 0, n}] &, n + 1, 0], {n, 0, 5}] (* Michael De Vlieger, Jul 21 2023 *)

allocatemem(234567890);
A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ Using code of Michel Marcus
A252738print(up_to_n) = { my(s, i=0, n=0); for(n=0, up_to_n, if(0 == n, s = 1, if(1 == n, s = 2; lev = vector(1); lev[1] = 2, oldlev = lev; lev = vector(2*length(oldlev)); s = 1; for(i = 0, (2^(n-1))-1, lev[i+1] = if((i%2),A003961(oldlev[(i\2)+1]),2*oldlev[(i\2)+1]); s *= lev[i+1]))); write("b252738.txt", n, " ", s)); }; \\ Counts them empirically.
A252738print(7);

(definec (A252738rec n) (if (<= n 1) (+ 1 n) (* (A000079 (A000079 (- n 2))) (A252738rec (- n 1)) (A003961 (A252738rec (- n 1)))))) ;; Implements the given recurrence; uses the memoizing definec-macro.
(define (A252738 n) (if (zero? n) 1 (mul A163511 (A000079 (- n 1)) (A000225 n))))
(define (mul intfun lowlim uplim) (let multloop ((i lowlim) (res 1)) (cond ((> i uplim) res) (else (multloop (+ 1 i) (* res (intfun i)))))))
;; Another alternative, implementing the new recurrence:
(definec (A252738 n) (if (<= n 1) (+ 1 n) (* (A267096 (- n 2)) (A000290 (A252738 (- n 1)))))) ;; Antti Karttunen, Feb 06 2016

a(0) = 1; a(1) = 2; for n > 1: a(n) = 2^(2^(n-2)) * a(n-1) * A003961(a(n-1)).
a(0) = 1; for n>=1: a(n) = Product_{k=A000079(n-1) .. A000225(n)} A163511(k) = Product_{k=2^(n-1) .. (2^n)-1} A163511(k).
a(0) = 1; a(1) = 2; for n > 1: a(n) = A267096(n-2) * a(n-1)^2. [Compare to the formulas of A191555] - Antti Karttunen, Feb 06 2016
From Michael De Vlieger, Jul 21 2023: (Start)
a(n) = Product_{k=1..n+1} prime(k)^e(n,k), where e(n,k) = k-th term in row n of A055248.
A067255(a(n)) = row n of A055248. (End)

Typos in the second formula corrected by Antti Karttunen, Feb 06 2016

A356300 Square array read by antidiagonals. A(n,k) is the nearest common ancestor of n and k in the binary tree depicted in A253563.

Original entry on oeis.org

1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 3, 2, 1, 1, 2, 2, 2, 2, 1, 1, 2, 3, 4, 3, 2, 1, 1, 2, 2, 2, 2, 2, 2, 1, 1, 2, 3, 4, 5, 4, 3, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 3, 4, 3, 4, 7, 4, 3, 4, 3, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1

Offset: 1

Antti Karttunen, Aug 03 2022

Array is symmetric and is read by antidiagonals as A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), ... .

Also the nearest common ancestor of n and k in the tree depicted in A253565 (the mirror image of the A253563-tree).

			The top left 21x21 corner of the array:
n/k  |  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21
-----+----------------------------------------------------------------------------
   1 |  1, 1, 1, 1, 1, 1, 1, 1, 1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,
   2 |  1, 2, 2, 2, 2, 2, 2, 2, 2,  2,  2,  2,  2,  2,  2,  2,  2,  2,  2,  2,  2,
   3 |  1, 2, 3, 2, 3, 2, 3, 2, 3,  2,  3,  2,  3,  2,  3,  2,  3,  2,  3,  2,  3,
   4 |  1, 2, 2, 4, 2, 4, 2, 4, 2,  4,  2,  4,  2,  4,  2,  4,  2,  4,  2,  4,  2,
   5 |  1, 2, 3, 2, 5, 2, 5, 2, 3,  2,  5,  2,  5,  2,  3,  2,  5,  2,  5,  2,  3,
   6 |  1, 2, 2, 4, 2, 6, 2, 4, 2,  6,  2,  4,  2,  6,  2,  4,  2,  6,  2,  4,  2,
   7 |  1, 2, 3, 2, 5, 2, 7, 2, 3,  2,  7,  2,  7,  2,  3,  2,  7,  2,  7,  2,  3,
   8 |  1, 2, 2, 4, 2, 4, 2, 8, 2,  4,  2,  8,  2,  4,  2,  8,  2,  4,  2,  8,  2,
   9 |  1, 2, 3, 2, 3, 2, 3, 2, 9,  2,  3,  2,  3,  2,  9,  2,  3,  2,  3,  2,  9,
  10 |  1, 2, 2, 4, 2, 6, 2, 4, 2, 10,  2,  4,  2, 10,  2,  4,  2,  6,  2,  4,  2,
  11 |  1, 2, 3, 2, 5, 2, 7, 2, 3,  2, 11,  2, 11,  2,  3,  2, 11,  2, 11,  2,  3,
  12 |  1, 2, 2, 4, 2, 4, 2, 8, 2,  4,  2, 12,  2,  4,  2,  8,  2,  4,  2, 12,  2,
  13 |  1, 2, 3, 2, 5, 2, 7, 2, 3,  2, 11,  2, 13,  2,  3,  2, 13,  2, 13,  2,  3,
  14 |  1, 2, 2, 4, 2, 6, 2, 4, 2, 10,  2,  4,  2, 14,  2,  4,  2,  6,  2,  4,  2,
  15 |  1, 2, 3, 2, 3, 2, 3, 2, 9,  2,  3,  2,  3,  2, 15,  2,  3,  2,  3,  2, 15,
  16 |  1, 2, 2, 4, 2, 4, 2, 8, 2,  4,  2,  8,  2,  4,  2, 16,  2,  4,  2,  8,  2,
  17 |  1, 2, 3, 2, 5, 2, 7, 2, 3,  2, 11,  2, 13,  2,  3,  2, 17,  2, 17,  2,  3,
  18 |  1, 2, 2, 4, 2, 6, 2, 4, 2,  6,  2,  4,  2,  6,  2,  4,  2, 18,  2,  4,  2,
  19 |  1, 2, 3, 2, 5, 2, 7, 2, 3,  2, 11,  2, 13,  2,  3,  2, 17,  2, 19,  2,  3,
  20 |  1, 2, 2, 4, 2, 4, 2, 8, 2,  4,  2, 12,  2,  4,  2,  8,  2,  4,  2, 20,  2,
  21 |  1, 2, 3, 2, 3, 2, 3, 2, 9,  2,  3,  2,  3,  2, 15,  2,  3,  2,  3,  2, 21,
.
A(3,6) = A(6,3) = 2 because the nearest common ancestor of 3 and 6 in the tree described in A253563 (and in A253565) is 2.
A(4,6) = A(6,4) = 4 because 6 occurs as a descendant of 4 in A253563-tree, thus their nearest common ancestor is 4 itself.

Index entries for sequences computed from indices in prime factorization

Cf. A253553, A253563, A253565, A356301.

Cf. also A348041.

up_to = 105;
A253553(n) = if(n<=2,1,my(f=factor(n), k=#f~); if(f[k,2]>1,f[k,2]--,f[k,1] = precprime(f[k,1]-1)); factorback(f));
A356300sq(x,y) = if(1==x||1==y,1, my(lista=List([]), i, k=x, stemvec, stemlen, h=y); while(k>1, listput(lista,k); k = A253553(k)); stemvec = Vecrev(Vec(lista)); stemlen = #stemvec; while(1, if((i=vecsearch(stemvec,h))>0, return(stemvec[i])); h = A253553(h)));
A356300list(up_to) = { my(v = vector(up_to), i=0); for(a=1,oo, for(col=1,a, i++; if(i > up_to, return(v)); v[i] = A356300sq(col,(a-(col-1))))); (v); };
v356300 = A356300list(up_to);
A356300(n) = v356300[n];

A356306 The nearest common ancestor of A000265(n) and gcd(A000265(n), sigma(n)) in the A253563-tree.

Original entry on oeis.org

1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 1, 1, 7, 1, 3, 1, 1, 3, 1, 1, 1, 1, 1, 1, 5, 1, 3, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 1, 3, 1, 1, 9, 7, 1, 1, 1, 5, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3

Offset: 1

Antti Karttunen, Aug 03 2022

nonn

Cf. A000203, A000265, A161942, A355931, A356300, A356301, A356307, A356308.

Cf. also A356156.

A000265(n) = (n>>valuation(n,2));
A161942(n) = A000265(sigma(n));
A253553(n) = if(n<=2,1,my(f=factor(n), k=#f~); if(f[k,2]>1,f[k,2]--,f[k,1] = precprime(f[k,1]-1)); factorback(f));
A356300sq(x,y) = if(1==x||1==y,1, my(lista=List([]), i, k=x, stemvec, stemlen, h=y); while(k>1, listput(lista,k); k = A253553(k)); stemvec = Vecrev(Vec(lista)); stemlen = #stemvec; while(1, if((i=vecsearch(stemvec,h))>0, return(stemvec[i])); h = A253553(h)));
A356306(n) = A356300sq(A000265(n), gcd(n, A161942(n)));

a(n) = A356300(A000265(n), A355931(n)).

A356307 The nearest common ancestor of A161942(n) and gcd(A000265(n), sigma(n)) in the A253563-tree.

Original entry on oeis.org

1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 1, 1, 7, 1, 3, 1, 1, 3, 1, 1, 1, 1, 1, 1, 3, 1, 3, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 7, 1, 1, 3, 1, 1, 9, 7, 1, 1, 1, 3, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3

Offset: 1

Antti Karttunen, Aug 04 2022

nonn

Cf. A000203, A000265, A161942, A253553, A355931, A356300, A356306, A356307.

Cf. also A356157.

A000265(n) = (n>>valuation(n,2));
A161942(n) = A000265(sigma(n));
A253553(n) = if(n<=2,1,my(f=factor(n), k=#f~); if(f[k,2]>1,f[k,2]--,f[k,1] = precprime(f[k,1]-1)); factorback(f));
A356300sq(x,y) = if(1==x||1==y,1, my(lista=List([]), i, k=x, stemvec, stemlen, h=y); while(k>1, listput(lista,k); k = A253553(k)); stemvec = Vecrev(Vec(lista)); stemlen = #stemvec; while(1, if((i=vecsearch(stemvec,h))>0, return(stemvec[i])); h = A253553(h)));
A356307(n) = A356300sq(A161942(n), gcd(n, A161942(n)));

a(n) = A356300(A161942(n), A355931(n)) = A356300(A161942(n), gcd(n, A161942(n))).

A369028 Exponential of Mangoldt function permuted by A253563.

Original entry on oeis.org

1, 2, 2, 3, 2, 1, 3, 5, 2, 1, 1, 1, 3, 1, 5, 7, 2, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 5, 1, 7, 11, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 7, 1, 11, 13, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1

Offset: 0

Antti Karttunen, Jan 12 2024

nonn

Also LCM-transform of A253563 (when viewed as an offset-1 sequence), because A253563 has the S-property explained in the comments of A368900.

Antti Karttunen, Table of n, a(n) for n = 0..65537
Index entries for sequences related to binary expansion of n

Cf. A014963, A054429, A368900, A369029, A369030, A369053.

A014963(n) = { ispower(n, , &n); if(isprime(n), n, 1); };
A061395(n) = if(1==n, 0, primepi(vecmax(factor(n)[, 1])));
A253550(n) = if(1==n, 1, (n/prime(A061395(n)))*prime(1+A061395(n)));
A253560(n) = if(1==n, 1, (n*prime(A061395(n))));
A253563(n) = if(n<2,(1+n),if(!(n%2),A253560(A253563(n/2)),A253550(A253563((n-1)/2))));
A369028(n) = A014963(A253563(n));

a(n) = A014963(A253563(n)).

a(1) = 0, and for n > 0, a(n) = lcm {1..A253563(n)} / lcm {1..A253563(n-1)}. [See comments]

A278533 a(n) = A046523(A253563(n)).

Original entry on oeis.org

1, 2, 4, 2, 8, 6, 4, 2, 16, 12, 12, 6, 8, 6, 4, 2, 32, 24, 36, 12, 24, 30, 12, 6, 16, 12, 12, 6, 8, 6, 4, 2, 64, 48, 72, 24, 72, 60, 36, 12, 48, 60, 60, 30, 24, 30, 12, 6, 32, 24, 36, 12, 24, 30, 12, 6, 16, 12, 12, 6, 8, 6, 4, 2, 128, 96, 144, 48, 216, 120, 72, 24, 144, 180, 180, 60, 72, 60, 36, 12, 96, 120, 180, 60, 120, 210, 60, 30, 48, 60, 60, 30, 24, 30, 12

Offset: 0

Antti Karttunen, Nov 30 2016

nonn

Antti Karttunen, Table of n, a(n) for n = 0..8191

Cf. A046523, A054429, A253563, A278222, A278531, A278535.

(define (A278533 n) (A046523 (A253563 n)))

a(n) = A046523(A253563(n)).

a(n) = A278535(A054429(n)).

A356301 The nearest common ancestor of A000265(sigma(n)) and A000265(n) in the tree depicted in A253563.

Original entry on oeis.org

1, 1, 1, 1, 3, 3, 1, 1, 3, 3, 3, 3, 7, 3, 3, 1, 3, 9, 5, 3, 1, 3, 3, 3, 5, 3, 3, 7, 3, 9, 1, 1, 3, 3, 3, 3, 19, 3, 3, 3, 3, 3, 11, 3, 9, 3, 3, 3, 3, 3, 9, 7, 3, 9, 3, 3, 3, 3, 3, 15, 31, 3, 3, 1, 3, 9, 17, 3, 3, 3, 3, 9, 37, 3, 3, 5, 3, 21, 5, 3, 3, 3, 3, 3, 3, 3, 15, 3, 3, 45, 7, 3, 1, 3, 3, 3, 7, 3, 9, 5, 3, 9, 13, 3, 3

Offset: 1

Antti Karttunen, Aug 03 2022

nonn

Antti Karttunen, Table of n, a(n) for n = 1..16384
Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
Index entries for sequences computed from indices in prime factorization
Index entries for sequences related to sigma(n)

Cf. A000203, A000265, A161942, A356300, A356301, A356306, A356307, A356308.
Cf. also A347879.
Positions of 1's in this sequence is given by the union of A000079 and A046528.

A000265(n) = (n>>valuation(n,2));
A161942(n) = A000265(sigma(n));
A253553(n) = if(n<=2,1,my(f=factor(n), k=#f~); if(f[k,2]>1,f[k,2]--,f[k,1] = precprime(f[k,1]-1)); factorback(f));
A356300sq(x,y) = if(1==x||1==y,1, my(lista=List([]), i, k=x, stemvec, stemlen, h=y); while(k>1, listput(lista,k); k = A253553(k)); stemvec = Vecrev(Vec(lista)); stemlen = #stemvec; while(1, if((i=vecsearch(stemvec,h))>0, return(stemvec[i])); h = A253553(h)));
A356301(n) = A356300sq(A161942(n),A000265(n));

a(n) = A356300(A161942(n), A000265(n)).

A356308 a(n) = gcd(n, A356301(n)), where A356301(n) is the nearest common ancestor of A000265(sigma(n)) and A000265(n) in the A253563-tree.

Original entry on oeis.org

1, 1, 1, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 9, 1, 1, 1, 1, 1, 3, 5, 1, 3, 7, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 9, 1, 1, 3, 1, 1, 3, 1, 1, 9, 1, 1, 3, 1, 1, 15, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 9, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 45, 7, 1, 1, 1, 1, 3, 1, 1, 9, 5, 1, 3, 1, 1, 3

Offset: 1

Antti Karttunen, Aug 04 2022

nonn

Cf. A000203, A000265, A161942, A253553, A356300, A356301, A356306, A356307.

Cf. also A356158.

A000265(n) = (n>>valuation(n,2));
A161942(n) = A000265(sigma(n));
A253553(n) = if(n<=2,1,my(f=factor(n), k=#f~); if(f[k,2]>1,f[k,2]--,f[k,1] = precprime(f[k,1]-1)); factorback(f));
A356300sq(x,y) = if(1==x||1==y,1, my(lista=List([]), i, k=x, stemvec, stemlen, h=y); while(k>1, listput(lista,k); k = A253553(k)); stemvec = Vecrev(Vec(lista)); stemlen = #stemvec; while(1, if((i=vecsearch(stemvec,h))>0, return(stemvec[i])); h = A253553(h)));
A356301(n) = A356300sq(A161942(n),A000265(n));
A356308(n) = gcd(n, A356301(n));

a(n) = gcd(n, A356301(n)).

A286533 Restricted growth sequence of A278533 (prime-signature of A253563).

Original entry on oeis.org

1, 2, 3, 2, 4, 5, 3, 2, 6, 7, 7, 5, 4, 5, 3, 2, 8, 9, 10, 7, 9, 11, 7, 5, 6, 7, 7, 5, 4, 5, 3, 2, 12, 13, 14, 9, 14, 15, 10, 7, 13, 15, 15, 11, 9, 11, 7, 5, 8, 9, 10, 7, 9, 11, 7, 5, 6, 7, 7, 5, 4, 5, 3, 2, 16, 17, 18, 13, 19, 20, 14, 9, 18, 21, 21, 15, 14, 15, 10, 7, 17, 20, 21, 15, 20, 22, 15, 11, 13, 15, 15, 11, 9, 11, 7, 5, 12, 13, 14, 9, 14, 15, 10, 7

Offset: 0

Antti Karttunen, May 17 2017

nonn

Antti Karttunen, Table of n, a(n) for n = 0..65537

Cf. A046523, A253563, A286531, A286535, A286622.

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])); }
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ This function from Charles R Greathouse IV, Aug 17 2011
A061395(n) = if(1==n, 0, primepi(vecmax(factor(n)[, 1]))); \\ After M. F. Hasler's code for A006530.
A253550(n) = if(1==n, 1, (n/prime(A061395(n)))*prime(1+A061395(n)));
A253560(n) = if(1==n, 1, (n*prime(A061395(n))));
A253563(n) = if(n<2,(1+n),if(!(n%2),A253560(A253563(n/2)),A253550(A253563((n-1)/2)))); \\ Would be better if memoized!
A278533(n) = A046523(A253563(n));
write_to_bfile(0,rgs_transform(vector(65538,n,A278533(n-1))),"b286533.txt");

A277331 a(n) = A253563(A003714(n)).

Original entry on oeis.org

1, 2, 4, 8, 6, 16, 12, 18, 32, 24, 36, 54, 30, 64, 48, 72, 108, 60, 162, 90, 150, 128, 96, 144, 216, 120, 324, 180, 300, 486, 270, 450, 750, 210, 256, 192, 288, 432, 240, 648, 360, 600, 972, 540, 900, 1500, 420, 1458, 810, 1350, 2250, 630, 3750, 1050, 1470, 512, 384, 576, 864, 480, 1296, 720, 1200, 1944, 1080, 1800, 3000, 840

Offset: 0

Antti Karttunen, Oct 12 2016

nonn

After the initial terms 1, 2 and 4, all other terms can be inductively generated by applying any finite composition-combination of A253560 and A253550 to 4, but with such a restriction that A253550 may not be applied twice in succession.

A permutation of A055932.

Antti Karttunen, Table of n, a(n) for n = 0..10946

Cf. A003714, A055932 (same sequence sorted into ascending order), A253550, A253560, A253563, A122111.

Cf. also A277006, A277332.

(define (A277331 n) (A253563 (A003714 n)))

a(n) = A253563(A003714(n)).

a(n) = A122111(A277006(n)).

cp's OEIS Frontend

A252738 Row products of irregular table A005940: a(0) = 1; a(1) = 2; for n > 1: 2^(2^(n-2)) * a(n-1) * A003961(a(n-1)); also row products of A163511, A253563, A253565, and A332977.

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A356300 Square array read by antidiagonals. A(n,k) is the nearest common ancestor of n and k in the binary tree depicted in A253563.

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A356306 The nearest common ancestor of A000265(n) and gcd(A000265(n), sigma(n)) in the A253563-tree.

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A356307 The nearest common ancestor of A161942(n) and gcd(A000265(n), sigma(n)) in the A253563-tree.

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A369028 Exponential of Mangoldt function permuted by A253563.

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A278533 a(n) = A046523(A253563(n)).

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A356301 The nearest common ancestor of A000265(sigma(n)) and A000265(n) in the tree depicted in A253563.

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A356308 a(n) = gcd(n, A356301(n)), where A356301(n) is the nearest common ancestor of A000265(sigma(n)) and A000265(n) in the A253563-tree.

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A286533 Restricted growth sequence of A278533 (prime-signature of A253563).