A333786 a(n) is the first occurrence of n in A332809.

1, 2, 3, 5, 6, 7, 11, 13, 14, 15, 23, 21, 29, 30, 31, 47, 33, 35, 61, 62, 75, 65, 66, 67, 71, 69, 93, 91, 131, 77, 134, 142, 133, 105, 139, 143, 141, 265, 154, 195, 366, 201, 266, 210, 161, 209, 213, 215, 355, 217, 335, 377, 299, 315, 319, 231, 322, 403, 419, 417, 431, 585, 329, 435, 429, 497, 638, 437, 631, 795

Offset: 1

Author

Michael De Vlieger, Peter Kagey, Antti Karttunen, Robert G. Wilson v, May 09 2020

Keywords

• nonn

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..15966 (first 1000 terms from Peter Kagey)

Crossrefs

Cf. A332809 (a left inverse).

Programs

Mathematica

a[n_] := Block[{lst = {{n}}}, While[ lst[[-1]] != {1}, lst = Join[lst, {Union[ Flatten[# - #/(First@# & /@ FactorInteger@#) & /@ lst[[-1]]]]}]]; Length@Flatten@lst]; t[] := 0; k = 1; While[k < 100001, b = a@k; If[ t[b] == 0, t[b] = k]; k++]; t@# & /@ Range@ 100 (* _Robert G. Wilson v, May 08 2020 *)

PARI

search_up_to = 20000;
A332809list(up_to) = { my(v=vector(up_to)); v[1] = Set([1]); for(n=2,up_to, my(f=factor(n)[, 1]~, s=Set([n])); for(i=1,#f,s = setunion(s,v[n-(n/f[i])])); v[n] = s); apply(length,v); }
v332809 = A332809list(search_up_to);
A332809(n) = v332809[n];
A333786list(search_up_to) = { my(focs=Map(),t); for(n=1,search_up_to,t = A332809(n); if(!mapisdefined(focs,t),mapput(focs,t,n))); my(lista=List([]),v); for(u=1,oo,if(!mapisdefined(focs,u,&v), return(Vec(lista)), listput(lista,v))); };
v333786 = A333786list(search_up_to);
A333786(n) = v333786[n]; \\ Antti Karttunen, May 09 2020

Python

from sympy import factorint
from functools import cache
from itertools import count, islice
@cache
def b(n): return {n}.union(*(b(n - n//p) for p in factorint(n)))
def A332809(n): return len(b(n))
def agen():
    adict, n = dict(), 1
    for k in count(1):
        v = A332809(k)
        if v not in adict: adict[v] = k
        while n in adict: yield adict[n]; n += 1
print(list(islice(agen(), 70))) # Michael S. Branicky, Aug 13 2022

Formula

A332809(a(n)) = n.