OFFSET
0,3
COMMENTS
Note that there are even terms besides 0, and they all seem to be squares: a(915) = 7744 (= 88^2), a(41844) = 611524 (= 782^2), a(58264) = 872356 (= 934^2), a(66936) = 1020100 (= 1010^2), a(95309) = 1503076 (= 1226^2), a(105456) = 1653796 (= 1286^2), ...
LINKS
Antti Karttunen, Table of n, a(n) for n = 0..110880
FORMULA
Other identities. For all n >= 0:
A155043(a(n)) = n.
MATHEMATICA
lim = 80; a[0] = 0; a[n_] := a[n] = 1 + a[n - DivisorSigma[0, n]]; t = Table[a@ n, {n, 0, 12 lim}]; Table[First@ Flatten@ Position[t, n] - 1, {n, 0, lim}] (* Michael De Vlieger, Sep 29 2015 *)
PROG
(PARI)
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)]);
A155043 = n -> if(!n, n, v155043[n]);
n=0; k=0; while(k <= 10000, if(A155043(n)==k, write("b261089.txt", k, " ", n); k++); n++; );
(Scheme, with Antti Karttunen's IntSeq-library, two variants)
(Haskell)
import Data.List (elemIndex); import Data.Maybe (fromJust)
a261089 = fromJust . (`elemIndex` a155043_list)
-- Reinhard Zumkeller, Nov 27 2015
CROSSREFS
Cf. A262505 (difference between the last and the first occurrence).
KEYWORD
nonn
AUTHOR
Antti Karttunen, Sep 23 2015
STATUS
approved