A060990 -id:A060990 - cp's OEIS frontend

A262686 a(n) = largest number k such that k - d(k) = n, or 0 if no such number exists, where d(n) = the number of divisors of n (A000005).

2, 4, 6, 5, 8, 7, 12, 0, 0, 11, 14, 16, 18, 0, 20, 17, 24, 21, 22, 0, 0, 23, 30, 27, 0, 0, 32, 36, 0, 33, 34, 35, 40, 0, 42, 39, 0, 0, 48, 45, 0, 43, 46, 0, 50, 47, 54, 51, 60, 0, 0, 55, 0, 57, 58, 0, 0, 64, 66, 61, 72, 65, 70, 0, 0, 69, 0, 0, 0, 75, 80, 73, 84, 77, 0, 0, 81, 79, 90, 0, 88, 85, 86, 87, 96, 0, 92, 91, 0, 93, 94, 100, 98, 99, 102, 97, 108, 105, 0, 101

Offset: 0

Antti Karttunen, Sep 28 2015

nonn

Antti Karttunen, Table of n, a(n) for n = 0..10080

Cf. A000005, A002183, A049820, A060990, A261100, A262512.

Cf. also A082284 (the smallest such number), A262511 (positions where these are equal and nonzero).

Table[k = 2 n + 3; While[Nor[k - DivisorSigma[0, k] == n, k == 0], k--]; k, {n, 0, 99}] (* Michael De Vlieger, Sep 29 2015 *)

(definec (A262686 n) (if (zero? n) 2 (let ((u (+ n (A002183 (+ 2 (A261100 n)))))) (let loop ((k u)) (cond ((= (A049820 k) n) k) ((< k n) 0) (else (loop (- k 1))))))))

A262507 a(n) = number of times n occurs in A155043.

Original entry on oeis.org

1, 2, 3, 5, 4, 5, 6, 4, 4, 4, 8, 4, 4, 5, 8, 7, 7, 7, 7, 8, 5, 6, 6, 8, 10, 7, 8, 7, 7, 5, 5, 6, 6, 8, 6, 7, 7, 7, 4, 5, 5, 6, 6, 8, 7, 5, 5, 6, 7, 11, 5, 4, 5, 8, 12, 7, 9, 5, 8, 8, 9, 10, 14, 11, 12, 11, 9, 11, 13, 12, 12, 11, 11, 11, 12, 12, 10, 9, 9, 9, 8, 6, 10, 9, 10, 8, 7, 7, 8, 11, 10, 10, 12, 9, 7, 6, 5, 5, 5, 5, 4, 7, 8, 6, 7, 9, 7, 5, 11, 13, 13, 8, 10, 12, 13, 10, 12, 16, 9, 8, 12

Offset: 0

Antti Karttunen, Sep 25 2015

nonn

Records are: 1, 2, 3, 5, 6, 8, 10, 11, 12, 14, 16, 17, 19, 21, 22, 24, 25, 26, 27, 31, 35, 39, 44, ... and they occur at positions: 0, 1, 2, 3, 6, 10, 24, 49, 54, 62, 117, 236, 445, 484, 892, 893, 1022, 1784, 1911, 1912, 1913, 20600, 50822, ...

a(n) gives the length of each row of irregular table A263265.

Antti Karttunen, Table of n, a(n) for n = 0..110880

Cf. A000005, A060990, A155043, A262502, A262505, A263265, A263270, A263279, A263280.
Cf. A261089, A262503.
Cf. A262508 (positions of ones).
Cf. A263260 (partial sums).

allocatemem(123456789);
uplim = 2162160; \\ = A002182(41).
v155043 = vector(uplim);
v155043[1] = 1; v155043[2] = 1;
for(i=3, uplim, v155043[i] = 1 + v155043[i-numdiv(i)]);
uplim2 = 110880; \\ = A002182(30).
v262507 = vector(uplim2);
for(i=1, uplim, if(v155043[i] <= uplim2, v262507[v155043[i]]++));
A262507 = n -> if(!n,1,v262507[n]);
for(n=0, uplim2, write("b262507.txt", n, " ", A262507(n)));

(define (A262507 n) (add (lambda (k) (if (= (A155043 k) n) 1 0)) n (A262502 (+ 2 n))))
;; Auxiliary function add implements sum_{i=lowlim..uplim} intfun(i)
(define (add intfun lowlim uplim) (let sumloop ((i lowlim) (res 0)) (cond ((> i uplim) res) (else (sumloop (1+ i) (+ res (intfun i)))))))

a(n) = Sum_{k=n..A262502(2+n)} [A155043(k) == n]. (Here [...] denotes the Iverson bracket, resulting 1 when A155043(k) is n and 0 otherwise.)
Other identities. For all n >= 0:
a(n) = A263279(n) + A263280(n).

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

Original entry on oeis.org

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.

A261100 a(n) is the greatest m for which A002182(m) <= n; the least monotonic left inverse for highly composite numbers A002182.

Original entry on oeis.org

1, 2, 2, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10

Offset: 1

Antti Karttunen, Sep 24 2015

nonn

Each n occurs A262501(n) times.

This is the only sequence w, which (1) satisfies w(A002182(n)) = n for all n >= 1 (thus is a left inverse of A002182), which (2) is monotonic (by necessity growing, although not strictly so), and which (3) is the lexicographically least of all sequences satisfying both (1) and (2). In other words, the largest number m for which A002182(m) <= n. - Antti Karttunen, Jun 06 2017

Antti Karttunen, Table of n, a(n) for n = 1..10080

Cf. A000005, A002182, A002183, A060990, A070319, A262501.

with(numtheory):
A261100_list := proc(len) local n, k, j, b, A, tn: A := NULL; k := 0;
for n from 1 to len do
    b := true; tn := tau(n);
    for j from 1 to n-1 while b do b := b and tau(j) < tn od:
    if b then k := k + 1 fi;
    A := A,k
od: A end: A261100_list(120); # Peter Luschny, Jun 06 2017

A002182 = Import["https://oeis.org/A002182/b002182.txt", "Table"];
inter = Interpolation[Reverse /@ A002182, InterpolationOrder -> 0];
A261100 = Rest[inter /@ Range[200]] - 1 (* Jean-François Alcover, Oct 25 2019 *)

v002182 = vector(1000); v002182[1] = 1; \\ For memoization.
A002182(n) = { my(d,k); if(v002182[n],v002182[n], k = A002182(n-1); d = numdiv(k); while(numdiv(k) <= d, k=k+1); v002182[n] = k; k); };
A261100(n) = { my(k=1); while(A002182(k)<=n,k=k+1); (k-1); } \\ Antti Karttunen, Jun 06 2017

(define (A261100 n) (let loop ((k 1)) (if (> (A002182 k) n) (- k 1) (loop (+ 1 k)))))

;; Requires Antti Karttunen's IntSeq-library.
(define A261100 (LEFTINV-LEASTMONO 1 1 A002182))

a(n) = the least k for which A002182(k+1) > n.
Other identities. For all n >= 1:
a(A002182(n)) = n. [The least monotonic sequence satisfying this condition.]
A070319(n) = A002183(a(n)).

Description clarified by Antti Karttunen, Jun 06 2017

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).

A262522 a(n)=0 if n is in A259934, otherwise the largest term in A045765 from which one can reach n by iterating A049820 zero or more times.

Original entry on oeis.org

0, 8, 0, 7, 8, 7, 0, 7, 8, 79, 20, 79, 0, 13, 20, 79, 24, 79, 0, 19, 20, 79, 0, 79, 24, 25, 40, 79, 28, 79, 0, 79, 40, 33, 0, 79, 36, 37, 140, 79, 40, 43, 0, 43, 50, 79, 0, 79, 140, 49, 50, 79, 52, 79, 0, 55, 56, 79, 0, 79, 140, 79, 0, 63, 64, 79, 66, 67, 68, 79, 0, 79, 140, 79, 74, 75, 123, 79, 0, 79, 88, 123, 98, 123, 140, 85, 98, 123, 88, 103, 0, 123, 98, 103, 0, 123

Offset: 0

Antti Karttunen, Oct 04 2015

nonn

If n is itself in A045765, we iterate 0 times, and thus a(n) = n.

			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. The largest term (which by necessity is always a term of A045765) is here 8, thus a(1) = 8. Note however that it is not always the largest leaf from which starts the longest path leading back to n. (In this case it is 7 instead of 8, see the example in A262695).
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}. The largest term is 79, thus a(9) = 79.

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

Cf. A000005, A045765, A049820, A060990, A082284, A259934, A262511, A262512, A262686, A262693.

Cf. A262679, A262695, A262696, A262697.

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) = n,
otherwise:
  a(n) = 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).
Other identities. For all n >= 1:
a(A262511(n)) = a(A262512(n)) = a(A082284(A262511(n))).

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)).

A236565 The smallest values m such that A049820(x) = m has exactly n solutions.

Original entry on oeis.org

7, 2, 0, 6, 22, 838, 17638, 192520, 3240114, 219476872, 2146772872, 24443168392, 1273061788552

Offset: 0

Jaroslav Krizek, Feb 09 2014

The 11 numbers x for which A049820(x) is equal to a(11) are a(11) + {12, 16, 24, 32, 36, 40, 56, 80, 96, 128, 512}. - Giovanni Resta, Feb 10 2014

			For n=4: 22 is the smallest identical value of A049820(x) for 4 distinct numbers x: 25, 26, 28, 30.

Cf. A049820, A236561, A236562, A236563, A060990.

a(7)-a(11) from Giovanni Resta, Feb 10 2014

a(12) from Ryan Tang, Jul 23 2025

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)).

cp's OEIS Frontend

A262686 a(n) = largest number k such that k - d(k) = n, or 0 if no such number exists, where d(n) = the number of divisors of n (A000005).

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A262507 a(n) = number of times n occurs in A155043.

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

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A261100 a(n) is the greatest m for which A002182(m) <= n; the least monotonic left inverse for highly composite numbers A002182.

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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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A262522 a(n)=0 if n is in A259934, otherwise the largest term in A045765 from which one can reach n by iterating A049820 zero or more times.

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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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