OFFSET
1,5
LINKS
J. M. Pedersen, Known amicable pairs.
FORMULA
An augmented amicable pair (m,n) is a pair of integers m, n with m<n and for which sigma(m)=sigma(n)=m+n-1
EXAMPLE
a(6)=9 because there are 9 augmented amicable pairs with m<=10^6
MATHEMATICA
s[n_]:=DivisorSigma[1, n]-n; AugmentedAmicableNumberQ[n_]:=If[s[s[n]+1]==n-1 && !DivisorSigma[1, n]==2n-1, True, False]; AugmentedAmicablePairList[ k_]:=(bnlist=Select[Range[k], AugmentedAmicableNumberQ[ # ]&]; newprlist= Table[Sort[{bnlist[[n]], s[bnlist[[n]]]+1}], {n, 1, Length[bnlist]}]; augamprlist=Union[newprlist, newprlist]); data=AugmentedAmicablePairList[10^7]; Table[Length[Select[data, First[ # ]<10^k &]], {k, 1, 7}]
CROSSREFS
KEYWORD
hard,nonn
AUTHOR
Ant King, Dec 20 2006
STATUS
approved