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!)
A126169 Smaller member of an infinitary amicable pair. 19
114, 594, 1140, 4320, 5940, 8640, 10744, 12285, 13500, 25728, 35712, 44772, 60858, 62100, 67095, 67158, 74784, 79296, 79650, 79750, 86400, 92960, 118500, 118944, 142310, 143808, 177750, 185368, 204512, 215712, 298188, 308220, 356408, 377784, 420640, 462330 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
A divisor of n is called infinitary if it is a product of divisors of the form p^{y_a 2^a}, where p^y is a prime power dividing n and sum_a y_a 2^a is the binary representation of y.
LINKS
Jan Munch Pedersen, Tables of Aliquot Cycles.
FORMULA
The values of m for which isigma(m)=isigma(n)=m+n and m<n.
EXAMPLE
a(5)=5940 because the fifth infinitary amicable pair is (5940,8460) and 5940 is its smallest member
MATHEMATICA
ExponentList[n_Integer, factors_List] := {#, IntegerExponent[n, # ]} & /@ factors; InfinitaryDivisors[1] := {1}; InfinitaryDivisors[n_Integer?Positive] := Module[ { factors = First /@ FactorInteger[n], d = Divisors[n] }, d[[Flatten[Position[ Transpose[ Thread[Function[{f, g}, BitOr[f, g] == g][ #, Last[ # ]]] & /@ Transpose[Last /@ ExponentList[ #, factors] & /@ d]], _?( And @@ # &), {1}]] ]] ] Null; properinfinitarydivisorsum[k_] := Plus @@ InfinitaryDivisors[k] - k; InfinitaryAmicableNumberQ[k_] := If[Nest[properinfinitarydivisorsum, k, 2] == k && ! properinfinitarydivisorsum[k] == k, True, False]; data1 = Select[ Range[10^6], InfinitaryAmicableNumberQ[ # ] &]; data2 = properinfinitarydivisorsum[ # ] & /@ data1; data3 = Table[{data1[[k]], data2[[k]]}, {k, 1, Length[data1]}]; data4 = Select[data3, First[ # ] < Last[ # ] &]; Table[First[data4[[k]]], {k, 1, Length[data4]}]
fun[p_, e_] := Module[{b = IntegerDigits[e, 2]}, m = Length[b]; Product[If[b[[j]] > 0, 1 + p^(2^(m - j)), 1], {j, 1, m}]]; infs[n_] := Times @@ (fun @@@ FactorInteger[n]) - n; s = {}; Do[k = infs[n]; If[k > n && infs[k] == n, AppendTo[s, n]], {n, 2, 10^5}]; s (* Amiram Eldar, Jan 22 2019 *)
CROSSREFS
Sequence in context: A251481 A251475 A292980 * A324708 A353746 A251459
KEYWORD
nonn
AUTHOR
Ant King, Dec 21 2006
EXTENSIONS
a(33)-a(36) from Amiram Eldar, Jan 22 2019
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 March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)