Modifications related to A001650

[David Wilson]

There are several OEIS sequences where a(n) counts the number of Z^d points 
in a d-ball of radius n. These are

A000012(n) for d = 0
A001650(n-1) for d = 1
A057655(n) for d = 2
A117609(n) for d = 3
A046895(n) for d = 4

You can see that A001650 is inconsistent, and would become consistent if 
reindexed starting at 0.  This would assist my goal of creating similar 
sequences up to d = 10 and providing b-files.  It also turns out that when 
A001650 is reindexed, its own formulas simply as well as others OEIS 
formulas that reference it. In short, A001650 "wants" to be indexed starting 
at 0.

Also, there are a few places where A001650 is a typo for A001065.

The following modifications to the OEIS database implement the proposed 
changes.

========================================================================
---- Replace ----
%F A001650 a(n) = 1 + 2*floor(sqrt(n-1)), n > 0. - Antonio Esposito 
(antonio.b.esposito(AT)italtel.it), Jan 21 2002
%F A001650 G.f.: theta_3(x)*x/(1-x). a(n+1)=a(n)+A000122(n). - Michael 
Somos, Apr 29 2003.
%o A001650 (PARI) a(n)=if(n<1,0,1+2*sqrtint(n-1))
%O A001650 1,2
---- with ----
%F A001650 a(n) = 1 + 2*floor(sqrt(n)) - Antonio Esposito 
(antonio.b.esposito(AT)italtel.it), Jan 21 2002
%F A001650 G.f.: theta_3(x)/(1-x). a(n)=a(n-1)+A000122(n). - Michael Somos, 
Apr 29 2003.
%o A001650 (PARI) a(n)=1+2*sqrtint(n)
%O A001650 0,2

========================================================================
---- Replace ----
%N A070015 Least m such that sum of aliquot parts of m [A001650(m)] equals n 
or 0 if no such number exists.
%F A070015 a(n)=Min{x; A001650(x)=n} or a(n)=0 if n is untouchable number 
(i.e. if from A005114)
%Y A070015 Cf. A000203, A001650, A048050, A051444, A007369, A070016, 
A005114, A048995.
---- with ----
%N A070015 Least m such that sum of aliquot parts of m [A001065(m)] equals n 
or 0 if no such number exists.
%F A070015 a(n)=Min{x; A001065(x)=n} or a(n)=0 if n is untouchable number 
(i.e. if from A005114)
%Y A070015 Cf. A000203, A001065, A048050, A051444, A007369, A070016, 
A005114, A048995.

========================================================================
---- Replace ----
%Y A069896 Cf. A048050, A000203, A001650.
---- with ----
%Y A069896 Cf. A048050, A000203, A001065.

========================================================================
---- Replace ----
%Y A070016 Cf. A000203, A001650, A048050, A051444, A007369, A070016, 
A005114, A048995.
---- with ----
%Y A070016 Cf. A000203, A001065, A048050, A051444, A007369, A070016, 
A005114, A048995.

========================================================================
---- Replace ----
%F A070010 a(n)=GCD[DivisorSigma[1, n+1]-(n+1), DivisorSigma[1, n]-n]= 
GCD[A001650(n+1), A001650(n)].
%Y A070010 Cf. A000203, A001650, GCD of various consecutive function values: 
A048586, A057467,
---- with ----
%F A070010 a(n)=GCD[DivisorSigma[1, n+1]-(n+1), DivisorSigma[1, n]-n]= 
GCD[A001065(n+1), A001065(n)].
%Y A070010 Cf. A000203, A001065, GCD of various consecutive function values: 
A048586, A057467,

========================================================================
---- Replace ----
%o A095875 (PARI) /* Using an existing program for A001650 ... */ A001650(n) 
= if(n<1,0,1+2*sqrtint(n-1)) /* and compensating for sequence offset 
differences */ a(n) = sum(k=1, n+1, A001650(k)) 
for(n=-1,100,print1(a(n),","))
---- with ----
%o A095875 (PARI) a(n) = sum(k=0, n, 1+2*sqrtint(n)) 
for(n=-1,100,print1(a(n),","))