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A192279 Anti-hypersigma(n): sum of the anti-divisors of n plus the recursive sum of the anti-divisors of the anti-divisors until 2 is reached.

%I A192279 #6 Mar 30 2012 18:53:49
%S A192279 2,5,7,9,19,17,17,40,33,37,45,40,67,49,89,96,65,88,71,134,127,91,189,
%T A192279 120,187,170,91,166,151,219,243,164,261,140,315,392,233,310,247,374,
%U A192279 245,150,461,280,285,347,407,468,215,538,515,234,565,422,609,532,495
%N A192279 Anti-hypersigma(n): sum of the anti-divisors of n plus the recursive sum of the anti-divisors of the anti-divisors until 2 is reached.
%C A192279 Similar to A191150 but using anti-divisors. The recursion is stopped when 2 is reached because 2 has no anti-divisors.
%H A192279 Paolo P. Lava, <a href="/A192279/b192279.txt">Table of n, a(n) for n = 3..5000</a>
%e A192279 n=14 -> anti-divisors are 3,4,9. We start with 3+4+9=16.
%e A192279 Now for 3, 4 and 9 we repeat the procedure:
%e A192279 3-> 2 -> no anti-divisors. To add: 2.
%e A192279 4-> 3 -> 2 -> no anti-divisors. To add: 3+2=5.
%e A192279 9-> 2,6. To add: 2+6=8.
%e A192279 --- 2 -> no anti-divisors.
%e A192279 --- 6 -> 4 -> 3 -> 2 -> no anti-divisors. To add: 4+3+2=9.
%e A192279 Total is 16+2+5+8+9=40.
%p A192279 with(numtheory);
%p A192279 P:=proc(n)
%p A192279 local a,b,c,k,s;
%p A192279 a:={};
%p A192279 for k from 2 to n-1 do if abs((n mod k)- k/2) < 1 then a:=a union {k}; fi;
%p A192279 od;
%p A192279 b:=nops(a); c:=op(a); s:=0;
%p A192279 if b>1 then
%p A192279   for k from 1 to b do s:=s+c[k]; od;
%p A192279 else s:=c;
%p A192279 fi;
%p A192279 b:=nops(a); c:=(sort([op(a)]));
%p A192279 for k from 1 to b do if c[k]>2 then s:=s+P(c[k]); fi; od;
%p A192279 s;
%p A192279 end:
%p A192279 Antihps:=proc(i)
%p A192279 local n;
%p A192279 for n from 1 to i do print(P(n)); od;
%p A192279 end:
%Y A192279 Cf. A066272, A191150.
%K A192279 nonn,easy
%O A192279 3,1
%A A192279 _Paolo P. Lava_, Jul 13 2011