login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A066505 f-amicable numbers where f(n) = n+1. 0
36, 62, 168, 326, 9936, 14056, 16198, 19862, 45304, 51910, 82662, 90152, 337688, 388102, 472902, 479672, 1970586, 2353756, 2969288, 3769942, 6319544, 8454886, 12276056, 13125574, 16783976, 17948854, 18818780, 20825882, 21738114, 22479040, 25960468, 31470614 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
f-amicable pairs are defined similarly to f-perfect numbers in A066218. That is, a, b is a f-amicable pair if f(a) = D(b) and f(b) = D(a), where D(n) = sum_{k divides n, k<n} f(d).
Pairs are (36,62), (14056,16198), (9936,19862), (45304,51910), (82662,90152) (337688,388102) and (472902,479672). The sequence shows them unbundled, then elements sorted according to size. - R. J. Mathar, Sep 07 2006, Dec 07 2006
LINKS
J. L. Pe, On a Generalization of Perfect Numbers, J. Rec. Math., 31(3) (2002-2003), 168-172.
EXAMPLE
Proper divisors of 36 = {1, 2, 3, 4, 6, 9, 12, 18}. f applied to these divisors = {2, 3, 4, 5, 7, 10, 13, 19}; their sum = 63. So D(36) = f(62). proper divisors of 62 = {1, 2, 31}. f applied to these divisors = {2, 3, 32}; their sum = 37. So D(62) = f(36). Therefore 36, 62 is an f-amicable pair.
MATHEMATICA
f[x_] := x + 1; d[x_] := Apply[ Plus, Map[ f, Divisors[ x] ] ] - f[ x]; m = Table[{x, y}, {x, 1, 1000}, {y, 1, 1000}]; Do[a = m[[i, j]]; If[ (a[[1]] < a[[2]]) && (f[a[[1]]] == d[a[[2]]]) && (f[a[[2]]] == d[a[[1]]]), Print[{i, j}]], {i, 1, 1000}, {j, 1, 1000}]
PROG
(C++) #include <limits.h> #include <iostream> #include <vector> using namespace std ; inline int f(const int n) { return n+1 ; } int D(const int n) { int resul=0 ; for(int k=1 ; k < n ; k++) if ( n %k == 0) resul += k+1 ; return resul ; } int main(int argc, char *argv[]) { vector<int> fvec ; vector<int> Dvec ; fvec.push_back(1) ; Dvec.push_back(1) ; for(int a=1 ; a < INT_MAX ; a++) { fvec.push_back( f(a)) ; Dvec.push_back( D(a)) ; for(int b=1 ; b< a ; b++) { if ( fvec[a]==Dvec[b] && fvec[b] == Dvec[a]) cout << b << ", " << a << ", " ; } } return 0 ; } - R. J. Mathar, Sep 07 2006
CROSSREFS
Sequence in context: A328961 A335295 A287862 * A039419 A043242 A044022
KEYWORD
nonn
AUTHOR
Joseph L. Pe, Jan 04 2002
EXTENSIONS
More terms from John W. Layman, Nov 11 2002
More terms from R. J. Mathar, Sep 07 2006
a(17)-a(32) from Donovan Johnson, Jun 23 2012
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 24 19:44 EDT 2024. Contains 373690 sequences. (Running on oeis4.)