A045765 -id:A045765 - cp's OEIS frontend

A236562 Numbers n such that A049820(x) = n has a solution.

0, 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 14, 15, 16, 17, 18, 21, 22, 23, 26, 27, 29, 30, 31, 32, 34, 35, 38, 39, 41, 42, 44, 45, 46, 47, 48, 51, 53, 54, 57, 58, 59, 60, 61, 62, 65, 69, 70, 71, 72, 73, 76, 77, 78, 80, 81, 82, 83, 84, 86, 87, 89, 90, 91, 92, 93, 94

Offset: 1

Jaroslav Krizek, Feb 09 2014

nonn

Complement of A045765.

			10 is in sequence because A049820(14) = 14 - A000005(14) = 14 - 4 = 10.

Jaroslav Krizek, Table of n, a(n) for n = 1..10000

Cf. A049820, A236561, A236565.

Take[Sort@ DeleteDuplicates@ Table[n - DivisorSigma[0, n], {n, 1200}], 67] (* Michael De Vlieger, Oct 13 2015 *)

A060990(a(n)) > 0.

A262697 a(n)=0 if n is in A259934, otherwise number of nodes (including leaves and the node n itself) in that finite subtree whose root is n and edge-relation is defined by A049820(child) = parent.

Original entry on oeis.org

0, 6, 0, 3, 2, 2, 0, 1, 1, 38, 3, 37, 0, 1, 2, 33, 2, 32, 0, 1, 1, 30, 0, 29, 1, 1, 3, 28, 1, 26, 0, 24, 2, 1, 0, 23, 1, 1, 16, 21, 1, 2, 0, 1, 2, 18, 0, 17, 13, 1, 1, 16, 1, 14, 0, 1, 1, 13, 0, 10, 11, 9, 0, 1, 1, 8, 1, 1, 1, 6, 0, 4, 10, 3, 1, 1, 23, 2, 0, 1, 2, 22, 4, 20, 9, 1, 3, 19, 1, 5, 0, 13, 2, 4, 0, 11, 8, 10, 1, 3, 1, 2, 0, 1, 6, 9, 0, 8, 1, 1, 2, 6, 1, 1, 0, 3, 1, 1, 0, 2, 5, 0, 12, 1

Offset: 0

Antti Karttunen, Oct 04 2015

nonn

			For n=1, its transitive closure (as defined by edge-relation A049820(child) = parent) is the union of {1} itself together with all its descendants, together {1, 3, 4, 5, 7, 8}. We see that there are no other nodes in a subtree whose root is 1, because A049820(3) = 3 - d(3) = 1, A049820(4) = 1, A049820(5) = 3, A049820(7) = 5, A049820(8) = 4 and both 7 and 8 are terms of A045765. Thus a(1) = 6.
For n=9, its transitive closure is {9, 11, 13, 15, 16, 17, 19, 21, 23, 24, 27, 29, 31, 33, 35, 36, 37, 39, 41, 43, 45, 47, 51, 53, 55, 57, 59, 61, 63, 64, 65, 67, 69, 71, 73, 75, 77, 79}, containing 38 terms, thus a(9) = 38.

Antti Karttunen, Table of n, a(n) for n = 0..17724

Cf. A000005, A045765, A049820, A060990, A082284, A259934, A262686, A262693.
Cf. A262679, A262522, A262695, A262696, A262890.
Cf. also A213727, A227643, A255327.

If A262693(n) = 1 [when n is in A259934],
  then a(n) = 0,
otherwise, if A060990(n) = 0 [when n is one of the leaves, A045765],
  then a(n) = 1,
otherwise:
  a(n) = 1 + Sum_{k = A082284(n) .. A262686(n)} [A049820(k) = n] * a(k).
(In the last clause [ ] stands for Iverson bracket, giving as its result 1 only when A049820(k) = n, and 0 otherwise).

A262695 a(n)=0 if n is in A259934, otherwise 1 + number of steps to reach the farthest leaf in that finite branch of the tree defined by edge-relation A049820(child) = parent.

Original entry on oeis.org

0, 4, 0, 3, 2, 2, 0, 1, 1, 24, 3, 23, 0, 1, 2, 22, 2, 21, 0, 1, 1, 20, 0, 19, 1, 1, 3, 18, 1, 17, 0, 16, 2, 1, 0, 15, 1, 1, 10, 14, 1, 2, 0, 1, 2, 13, 0, 12, 9, 1, 1, 11, 1, 10, 0, 1, 1, 9, 0, 8, 8, 7, 0, 1, 1, 6, 1, 1, 1, 5, 0, 4, 7, 3, 1, 1, 13, 2, 0, 1, 2, 12, 4, 11, 6, 1, 3, 10, 1, 5, 0, 9, 2, 4, 0, 8, 5, 7, 1, 3, 1, 2, 0, 1, 4, 6, 0, 5, 1, 1, 2, 4, 1, 1, 0, 3, 1, 1, 0, 2, 3

Offset: 0

Antti Karttunen, Oct 04 2015

nonn

			For n=1, its transitive closure (as defined by edge-relation A049820(child) = parent) is the union of {1} itself together with all its descendants: {1, 3, 4, 5, 7, 8}. We see that there are no other nodes in this subtree whose root is 1, because A049820(3) = 3 - d(3) = 1, A049820(4) = 1, A049820(5) = 3, A049820(7) = 5, A049820(8) = 4 and of these only 7 and 8 are terms of A045765 (leaves). Starting iterating from 7 with A049820, we get 7 -> 5, 5 -> 3, 3 -> 1, and starting from 8 we get 8 -> 4, 4 -> 1, of which the former path is longer (3 steps), thus a(1) = 3+1 = 4.
For n=9, its transitive closure is {9, 11, 13, 15, 16, 17, 19, 21, 23, 24, 27, 29, 31, 33, 35, 36, 37, 39, 41, 43, 45, 47, 51, 53, 55, 57, 59, 61, 63, 64, 65, 67, 69, 71, 73, 75, 77, 79}. In this case the longest path is obtained by starting iterating from the largest of these: 79 -> 77 -> 73 -> 71 -> 69 -> 65 -> 61 -> 59 -> 57 -> 53 -> 51 -> 47 -> 45 -> 39 -> 35 -> 31 -> 29 -> 27 -> 23 -> 21 -> 17 -> 15 -> 11 -> 9, which is 23 steps long, thus a(9) = 23+1 = 24.

Antti Karttunen, Table of n, a(n) for n = 0..17724

Cf. A000005, A045765, A049820, A060990, A082284, A259934, A262686, A262693.
Cf. A262522, A262696, A262697.
Cf. also A213725.

If A262693(n) = 1 [when n is in A259934],
  then a(n) = 0,
otherwise, if A060990(n) = 0 [when n is one of the leaves, A045765],
  then a(n) = 1,
otherwise:
  a(n) = 1 + Max_{k = A082284(n) .. A262686(n)} [A049820(k) = n] * a(k).
(In the last clause [ ] stands for Iverson bracket, giving as its result 1 only when A049820(k) = n, and 0 otherwise).

A262696 a(n)=0 if n is in A259934, otherwise number of terminal nodes (including n itself if it is a leaf) in that finite subtree whose root is n and whose edge-relation is defined by A049820(child) = parent.

Original entry on oeis.org

0, 2, 0, 1, 1, 1, 0, 1, 1, 13, 1, 13, 0, 1, 1, 11, 1, 11, 0, 1, 1, 10, 0, 10, 1, 1, 1, 10, 1, 9, 0, 8, 1, 1, 0, 8, 1, 1, 6, 7, 1, 1, 0, 1, 1, 6, 0, 6, 5, 1, 1, 6, 1, 5, 0, 1, 1, 5, 0, 3, 4, 3, 0, 1, 1, 3, 1, 1, 1, 2, 0, 1, 4, 1, 1, 1, 7, 1, 0, 1, 1, 7, 1, 6, 4, 1, 1, 6, 1, 1, 0, 5, 1, 1, 0, 4, 4, 4, 1, 1, 1, 1, 0, 1, 3, 4, 0, 4, 1, 1, 1, 3, 1, 1, 0, 1, 1, 1, 0, 1, 3, 0, 4, 1

Offset: 0

Antti Karttunen, Oct 04 2015

nonn

			For n=1, its transitive closure (as defined by edge-relation A049820(child) = parent) is the union of {1} itself together with all its descendants: {1, 3, 4, 5, 7, 8}. We see that there are no other nodes in a subtree whose root is 1, because A049820(3) = 3 - d(3) = 1, A049820(4) = 1, A049820(5) = 3, A049820(7) = 5, A049820(8) = 4 and of these only 7 and 8 are terms of A045765. Thus a(1) = 2.
For n=9, its transitive closure is {9, 11, 13, 15, 16, 17, 19, 21, 23, 24, 27, 29, 31, 33, 35, 36, 37, 39, 41, 43, 45, 47, 51, 53, 55, 57, 59, 61, 63, 64, 65, 67, 69, 71, 73, 75, 77, 79}, of which only thirteen members: {13, 19, 24, 33, 36, 37, 43, 55, 63, 64, 67, 75, 79} are leaves (in A045765), thus a(9) = 13.

Antti Karttunen, Table of n, a(n) for n = 0..17724

Cf. A000005, A045765, A049820, A060990, A082284, A259934, A262686, A262693.
Cf. A262522, A262695, A262697.
Cf. also A213726.

If A262693(n) = 1 [when n is in A259934],
  then a(n) = 0,
otherwise, if A060990(n) = 0 [when n is one of the leaves, A045765],
  then a(n) = 1,
otherwise:
  a(n) = Sum_{k = A082284(n) .. A262686(n)} [A049820(k) = n] * a(k).
(In the last clause [ ] stands for Iverson bracket, giving as its result 1 only when A049820(k) = n, and 0 otherwise).
Other identities:
For any n in A262511 but not in A259934, a(n) = a(A082284(n)).

A262901 Numbers that have at least one leaf-child in the tree generated by edge-relation A049820(child) = parent.

Original entry on oeis.org

4, 5, 11, 14, 16, 17, 22, 27, 29, 32, 35, 41, 44, 46, 48, 51, 57, 58, 62, 65, 69, 70, 77, 80, 81, 91, 92, 96, 101, 102, 107, 110, 111, 114, 118, 119, 120, 128, 129, 130, 138, 139, 141, 144, 147, 148, 152, 155, 158, 161, 162, 165, 166, 169, 176, 181, 187, 191, 192, 199, 201, 214, 215, 216, 222, 224, 227, 231, 234, 238, 239, 247, 248, 249, 255, 258, 262, 264, 269, 277, 278, 282, 286, 291, 294, 296

Offset: 1

Antti Karttunen, Oct 06 2015

nonn

Positions of nonzeros in A262900.
Numbers n such that there is at least one k such that k - d(k) = n [where d(k) is the number of divisors of k, A000005(k)], but there is no such x that x - d(x) = k, in other words, k is one of the terms of A045765.
Sequence A262902 sorted into ascending order, with duplicates removed.

Antti Karttunen, Table of n, a(n) for n = 1..10000

Cf. A000005, A045765, A049820, A262900, A262902.
Cf. A262903 (a subsequence).
Subsequence of A236562.
Cf. also A257508.

A265751 Square array A(row,col): A(row,0) = row and for col >= 1, if A082284(row) is 0, then A(row,col) = 0, otherwise A(row,col) = A(A082284(row),col-1).

Original entry on oeis.org

0, 1, 1, 3, 3, 2, 5, 5, 6, 3, 7, 7, 9, 5, 4, 0, 0, 11, 7, 8, 5, 0, 0, 13, 0, 0, 7, 6, 0, 0, 0, 0, 0, 0, 9, 7, 0, 0, 0, 0, 0, 0, 11, 0, 8, 0, 0, 0, 0, 0, 0, 13, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13, 14, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, 13, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18, 13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 22, 0, 14

Offset: 0

Antti Karttunen, Dec 21 2015

The square array A(row>=0, col>=0) is read by downwards antidiagonals as: A(0,0), A(0,1), A(1,0), A(0,2), A(1,1), A(2,0), A(0,3), A(1,2), A(2,1), A(3,0), ...

Each row n lists all the nodes in A263267-tree that one encounters when one starts from node with number n and always chooses the smallest possible child of it [given by A082284(n)], and then the smallest possible child of that child, etc, until a leaf-child (one of the terms of A045765) is encountered, after which the rest of the row contains only zeros.

			The top left corner of the array:
   0,  1,  3,  5,  7,  0,  0,  0,  0
   1,  3,  5,  7,  0,  0,  0,  0,  0
   2,  6,  9, 11, 13,  0,  0,  0,  0
   3,  5,  7,  0,  0,  0,  0,  0,  0
   4,  8,  0,  0,  0,  0,  0,  0,  0
   5,  7,  0,  0,  0,  0,  0,  0,  0
   6,  9, 11, 13,  0,  0,  0,  0,  0
   7,  0,  0,  0,  0,  0,  0,  0,  0
   8,  0,  0,  0,  0,  0,  0,  0,  0
   9, 11, 13,  0,  0,  0,  0,  0,  0
  10, 14, 20,  0,  0,  0,  0,  0,  0
  11, 13,  0,  0,  0,  0,  0,  0,  0
  12, 18, 22, 25,  0,  0,  0,  0,  0
  13,  0,  0,  0,  0,  0,  0,  0,  0
  14, 20,  0,  0,  0,  0,  0,  0,  0
  15, 17, 19,  0,  0,  0,  0,  0,  0
  16, 24,  0,  0,  0,  0,  0,  0,  0
  17, 19,  0,  0,  0,  0,  0,  0,  0
  18, 22, 25,  0,  0,  0,  0,  0,  0
  19,  0,  0,  0,  0,  0,  0,  0,  0
  20,  0,  0,  0,  0,  0,  0,  0,  0
  21, 23, 27, 29, 31, 35, 37,  0,  0
  22, 25,  0,  0,  0,  0,  0,  0,  0
  23, 27, 29, 31, 35, 37,  0,  0,  0
  ...
Starting from n = 21, we get the following chain: 21 -> 23 -> 27 -> 29 -> 31 -> 35 -> 37, with A082284 iterated 6 times before the final nonzero term 37 (for which A060990(37) = A082284(37) = 0) is encountered. Thus the row 21 of array contains terms 21, 23, 27, 29, 31, 35, 37, followed by an infinite number of zeros.

Cf. also A000005, A045765, A060990.
Column 0: A001477, Column 1: A082284.
Cf. A266111 (number of significant terms on each row, without the trailing zeros).
Cf. A266116 (the rightmost term before trailing zeros).
See also array A263271 constructed in the same way, but obtained by following always the largest child A262686, instead of the smallest child A082284.
Cf. also tree A263267 (and its illustration).

(define (A265751 n) (A265751bi (A002262 n) (A025581 n)))
(define (A265751bi row col) (cond ((zero? col) row) ((A082284 row) => (lambda (lad) (if (zero? lad) lad (A265751bi lad (- col 1)))))))
;; Alternatively:
(define (A265751bi row col) (cond ((zero? col) row) ((and (zero? row) (= 1 col)) 1) ((zero? (A265751bi row (- col 1))) 0) (else (A082284 (A265751bi row (- col 1))))))

A(row,0) = row and for col >= 1, if A082284(row) is 0, then A(row,col) = 0, otherwise A(row,col) = A(A082284(row),col-1).

A(0,0) = 0, A(0,1) = 1; if col = 0, A(row,0) = row; and for col > 0, if A(row,col-1) = 0, then A(row,col) = 0, otherwise A(row,col) = A082284(A(row,col-1)).

A263081 a(n) = largest k for which A155043(k) < A262508(n); a(n) = A262509(n) + A262909(n).

Original entry on oeis.org

124340, 124340, 124340, 124340, 124340, 124340, 124340, 124340, 124340, 124340, 124340, 124340, 124340, 124340, 124340, 124340, 124340, 124340, 124340, 124340, 124340, 124340, 124340, 124340, 124340, 124340, 124340, 124340, 124340, 124340, 124340, 124340, 124340, 124340, 124340, 124340, 124340, 124340, 24684000, 24684000, 24684000, 24684000, 24684000, 24684000, 24684000

Offset: 1

Antti Karttunen, Oct 09 2015

nonn

a(n) = largest k for which A155043(k) < A155043(A262509(n)).
If a(n) > A262509(n) then it must be a leaf (see comments in A262909 for why). Particularly, we have A045765(40722) = 124340, A045765(8191770) = 24684000.
Terms of sequence (together with the corresponding values in A262508) give particularly clean values for the boundaries that are used for example in the C++-program which computes A262896.

Antti Karttunen, Table of n, a(n) for n = 1..68

Cf. A045765, A155043, A262508, A262509, A262896, A262909, A263077, A263083.

(define (A263081 n) (+ (A262509 n) (A262909 n)))

a(n) = A263077(A262509(n)).

a(n) = A262509(n) + A262909(n).

A263091 Primes p for which A049820(x) = p has no solution.

Original entry on oeis.org

7, 13, 19, 37, 43, 67, 79, 103, 109, 113, 131, 163, 167, 193, 229, 241, 251, 257, 271, 293, 307, 313, 353, 359, 379, 383, 397, 401, 439, 463, 479, 487, 491, 499, 503, 509, 563, 571, 647, 653, 661, 673, 701, 739, 743, 757, 761, 773, 823, 859, 863, 883, 887, 911, 937, 941, 953, 967, 971, 977, 983, 1009, 1093, 1103, 1109, 1171, 1181, 1193, 1217, 1279, 1283, 1291, 1297, 1307, 1321, 1361

Offset: 1

Antti Karttunen, Oct 11 2015

nonn

Primes p that there is no such k for which k - d(k) = p, where d(k) is the number of divisors of k (A000005).

Antti Karttunen, Table of n, a(n) for n = 1..15383

Complement among primes: A263090.
Intersection of A000040 and A045765.
Subsequence of A067774 (A049591).
Cf. A000005, A049820, A060990.

lim = 10000; s = Select[Complement[Range@ lim, Sort@ DeleteDuplicates@ Table[n - DivisorSigma[0, n], {n, lim}]], PrimeQ]; Take[s, 76] (* Michael De Vlieger, Oct 13 2015 *)

allocatemem(123456789);
uplim1 = 2162160 + 320; \\ = A002182(41) + A002183(41).
v060990 = vector(uplim1);
for(n=3, uplim1, v060990[n-numdiv(n)]++);
A060990 = n -> if(!n,2,v060990[n]);
n=0; forprime(p=2, 524287, if((0 == A060990(p)), n++; write("b263091.txt", n, " ", p)));

;; With Antti Karttunen's IntSeq-library.
(define A263091 (MATCHING-POS 1 1 (lambda (n) (and (= 1 (A010051 n)) (zero? (A060990 n))))))

A262909 a(n) = greatest k such that A155043(k+A262509(n)) < A155043(A262509(n)).

Original entry on oeis.org

5197, 5193, 5177, 5115, 5113, 4419, 4417, 4259, 4245, 4243, 4239, 4059, 4047, 3991, 3941, 3633, 3593, 3449, 3445, 3437, 3423, 3421, 2897, 2789, 2517, 2261, 2079, 2077, 2067, 2063, 1527, 1379, 1135, 1127, 1117, 1103, 1083, 575, 23457, 23451, 21689, 21671, 20241, 19003, 18977, 18649, 18063, 18019, 14853, 14159, 13659, 12707, 11681, 10993, 10991, 10297, 10281, 9151, 9149, 9145, 9111, 8897, 8535, 8147, 6835, 6813, 5539, 5537

Offset: 1

Antti Karttunen, Oct 09 2015

nonn

a(n) = largest k such that A155043(k+A262509(n)) < A262508(n).
There might occur also negative terms, but no zeros.
For all terms a(n) > 0, a(n)+A262509(n) = A263081(n) is by necessity one of the leaves (A045765) in the tree generated by edge-relation A049820(child) = parent. See also comments in A262908.

Cf. A000005, A049820, A045765, A262508, A262509, A262908, A263078, A263081.

a(n) = A263078(A262509(n)).
a(n) = A263081(n) - A262509(n).
Other identities. For all n >= 1:
a(n) >= A262908(n).

A263271 Square array A(row,col): A(row,0) = row and for col >= 1, if A262686(row) is 0, then A(row,col) = 0, otherwise A(row,col) = A(A262686(row),col-1).

Original entry on oeis.org

0, 2, 1, 6, 4, 2, 12, 8, 6, 3, 18, 0, 12, 5, 4, 22, 0, 18, 7, 8, 5, 30, 0, 22, 0, 0, 7, 6, 34, 0, 30, 0, 0, 0, 12, 7, 42, 0, 34, 0, 0, 0, 18, 0, 8, 46, 0, 42, 0, 0, 0, 22, 0, 0, 9, 54, 0, 46, 0, 0, 0, 30, 0, 0, 11, 10, 58, 0, 54, 0, 0, 0, 34, 0, 0, 16, 14, 11

Offset: 0

Antti Karttunen, Nov 29 2015

The square array A(row>=0, col>=0) is read by downwards antidiagonals as: A(0,0), A(0,1), A(1,0), A(0,2), A(1,1), A(2,0), A(0,3), A(1,2), A(2,1), A(3,0), ...

Each row n lists all the nodes in A263267-tree that one encounters when one starts from node n and always chooses the largest possible child of it (A262686), and then the largest possible child of that child, etc, until a leaf-child (one of the terms of A045765) is encountered, after which the rest of the row contains only zeros.

			The top left corner of the array:
   0,  2,  6, 12, 18, 22, 30, 34, 42, 46, 54, 58, 66,  0,  0,  0,  0
   1,  4,  8,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0
   2,  6, 12, 18, 22, 30, 34, 42, 46, 54, 58, 66,  0,  0,  0,  0,  0
   3,  5,  7,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0
   4,  8,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0
   5,  7,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0
   6, 12, 18, 22, 30, 34, 42, 46, 54, 58, 66,  0,  0,  0,  0,  0,  0
   7,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0
   8,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0
   9, 11, 16, 24,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0
  10, 14, 20,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0
  11, 16, 24,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0
  12, 18, 22, 30, 34, 42, 46, 54, 58, 66,  0,  0,  0,  0,  0,  0,  0
  13,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0
  14, 20,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0
  15, 17, 21, 23, 27, 36,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0
  ...

Antti Karttunen, Table of n, a(n) for n = 0..10439; the first 144 antidiagonals

Column 0: A001477, Column 1: A262686.
Cf. A264971 (number of significant terms on each row, position where the first trailing zero-term occurs).
Cf. A264970.
Cf. also A000005, A045765, A263267.
See also array A265751 constructed in the same way, but obtained by following always the smallest child A082284, instead of the largest child A262686.

(define (A263271 n) (A263271bi (A002262 n) (A025581 n)))
(define (A263271bi row col) (cond ((zero? col) row) ((A262686 row) => (lambda (lad) (if (zero? lad) lad (A263271bi lad (- col 1)))))))
;; An alternative implementation, reflecting the new recurrence:
(define (A263271bi row col) (cond ((zero? col) row) ((and (zero? row) (= 1 col)) 2) ((zero? (A263271bi row (- col 1))) 0) (else (A262686 (A263271bi row (- col 1))))))

A(row,0) = row and for col >= 1, if A262686(row) is 0, then A(row,col) = 0, otherwise A(row,col) = A(A262686(row),col-1).

A(0,0) = 0, A(0,1) = 2; if col = 0, A(row,0) = row; and for col > 0, if A(row,col-1) = 0, then A(row,col) = 0, otherwise A(row,col) = A262686(A(row,col-1)). [Another, perhaps more intuitive recurrence for this array.] - Antti Karttunen, Dec 21 2015

cp's OEIS Frontend

A236562 Numbers n such that A049820(x) = n has a solution.

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A262697 a(n)=0 if n is in A259934, otherwise number of nodes (including leaves and the node n itself) in that finite subtree whose root is n and edge-relation is defined by A049820(child) = parent.

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A262695 a(n)=0 if n is in A259934, otherwise 1 + number of steps to reach the farthest leaf in that finite branch of the tree defined by edge-relation A049820(child) = parent.

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A262696 a(n)=0 if n is in A259934, otherwise number of terminal nodes (including n itself if it is a leaf) in that finite subtree whose root is n and whose edge-relation is defined by A049820(child) = parent.

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A262901 Numbers that have at least one leaf-child in the tree generated by edge-relation A049820(child) = parent.

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A265751 Square array A(row,col): A(row,0) = row and for col >= 1, if A082284(row) is 0, then A(row,col) = 0, otherwise A(row,col) = A(A082284(row),col-1).

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A263081 a(n) = largest k for which A155043(k) < A262508(n); a(n) = A262509(n) + A262909(n).

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A263091 Primes p for which A049820(x) = p has no solution.

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A262909 a(n) = greatest k such that A155043(k+A262509(n)) < A155043(A262509(n)).

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