OFFSET
0,2
COMMENTS
The first odd terms occur as a(121) = 1089, a(123) = 1093, a(349) = 3253, a(717) = 7581, a(807) = 8685, a(1225) = 13689, etc.
LINKS
Antti Karttunen, Table of n, a(n) for n = 0..110880
FORMULA
Other identities and observations. For all n >= 0:
A262502(n+2) > a(n). [Not rigorously proved, but empirical evidence and common sense agrees.]
MATHEMATICA
lim = 80; a[0] = 0; a[n_] := a[n] = 1 + a[n - DivisorSigma[0, n]]; t = Table[a@ n, {n, 0, 12 lim}]; Last@ Flatten@ Position[t, #] - 1 & /@ Range[0, lim] (* Uses the product of a limit and an arbitrary coefficient (12) based on observation of output for low values (n < 500). This might need to be adjusted for large n to give correct values of a(n). - Michael De Vlieger, Sep 29 2015 *) (* Note: one really should use a general safe limit, like A262502(n+2) I use in my Scheme-program. - Antti Karttunen, 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]);
uplim2 = 110880; \\ = A002182(30).
v262503 = vector(uplim2);
for(i=1, uplim, if(v155043[i] <= uplim2, v262503[v155043[i]] = i));
A262503 = n -> if(!n, n, v262503[n]);
for(n=0, uplim2, write("b262503.txt", n, " ", A262503(n)));
(Scheme)
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Sep 24 2015
STATUS
approved