This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
import Data.List (genericIndex) a155043 n = genericIndex a155043_list n a155043_list = 0 : map ((+ 1) . a155043) a049820_list -- Reinhard Zumkeller, Nov 27 2015
with(numtheory): a := proc (n) if n = 0 then 0 else 1+a(n-tau(n)) end if end proc: seq(a(n), n = 0 .. 90); # Emeric Deutsch, Jan 26 2009
a[0] = 0; a[n_] := a[n] = 1 + a[n - DivisorSigma[0, n]]; Table[a@n, {n, 0, 82}] (* Michael De Vlieger, Sep 24 2015 *)
uplim = 110880; \\ = A002182(30). v155043 = vector(uplim); v155043[1] = 1; v155043[2] = 1; for(i=3, uplim, v155043[i] = 1 + v155043[i-numdiv(i)]); A155043 = n -> if(!n,n,v155043[n]); for(n=0, uplim, write("b155043.txt", n, " ", A155043(n))); \\ Antti Karttunen, Sep 23 2015
from sympy import divisor_count as d def a(n): return 0 if n==0 else 1 + a(n - d(n)) print([a(n) for n in range(101)]) # Indranil Ghosh, Jun 03 2017
(definec (A155043 n) (if (zero? n) n (+ 1 (A155043 (A049820 n))))) ;; Antti Karttunen, Sep 23 2015
Rows 0 - 21 of the table. The lines show the nodes of the tree connected by the edge-relation A049820(child) = parent:
0;
| \
1, 2;
| \ \
3, 4, 6;____
| | | \ \
5, 8, 9, 10, 12;
| | | |
7, _ 11, 14, 18;
/ | \ \ \
13, 15, 16, 20, 22;____
| | / | \ \
17, 24, 25, 26, 28, 30;
| \ | |
19, 21, 32, 34;
| | | \
23, 40, 38, 42;____
| | \ \
27, 44, 48, 46;____
| \ | | \ | \ \
29, 36, 50, 56, 60, 49, 52, 54;
| \ | |
31, 33, 72, 58;
| | | \
35, 84, 62, 66;
| \ | | \
37, 39, 96, 68, 70;_______
| \ | \ / | \ \
41, 45, 104, 108, 74, 76, 78, 80;
| | | | | \ \
43, 47, 120, _81, 82, 90, 88;
| | \ / | | |
51, 128, 132, 83, 85, 86, 94;
| \ | \ | | |
53, 55 136, 140 87, 92, 102;______
| | \ | | \ \
57,_ 89, 91, 98, 106, 110, 112;
/ | \ / / \ | |
59, 63, 64, 93, 95, 100, 114, 116;
| | | | \
61, 99, 97, _118, 126;
| | | / | \
65, 101, 105, 121, 122, 124;
(See also _Michael De Vlieger_'s poster in the Links section.)
uplim = 125753; \\ = A263260(10001). checklimit = 1440; \\ Hard limit 1440 good for at least up to A002182(67) = 1102701600 as A002183(67) = 1440. v263267 = vector(uplim); A263267 = n -> if(!n,n,v263267[n]); z = 0; for(n=0, uplim, t = A263267(n); write("b263267.txt", n, " ", t); for(k=t+1, t+checklimit, if((k-numdiv(k)) == t, z++; if(z <= uplim, v263267[z] = k))));
# After David Eppstein's Python-code for A088975. def A263267(): '''Breadth-first reading of irregular tree defined by the edge-relation A049820(child) = parent''' yield 0 for x in A263267(): for k in [x+1 .. 2*(x+1)]: if ((k - sloane.A000005(k)) == x): yield k def take(n,g): '''Returns a list composed of the next n elements returned by generator g.''' return [next(g) for _ in range(n)] take(120, A263267())
;; This version creates the list of terms incrementally, using append! function that physically modifies the list at the same time as it is traversed. Otherwise the idea is essentially the same as with Python/Sage-program above: (define (A263267list_up_to_n_terms_at_least n) (let ((terms-produced (list 0))) (let loop ((startp terms-produced) (endp terms-produced) (k (- n 1))) (cond ((<= k 0) terms-produced) (else (let ((children (children-of-n-in-A049820-tree (car startp)))) (cond ((null? children) (loop (cdr startp) endp k)) (else (begin (append! endp children) (loop (cdr startp) children (- k (length children)))))))))))) (define (children-of-n-in-A049820-tree n) (let loop ((k (A262686 n)) (children (list))) (cond ((<= k n) children) ((= (A049820 k) n) (loop (- k 1) (cons k children))) (else (loop (- k 1) children)))))
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)))))))
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