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 A126175 Larger member of an augmented infinitary amicable pair. 8
 1483785, 2479065, 2580105, 4895241, 7336455, 9100905, 10350345, 16367481, 17307105, 24829945, 15706090, 27866241, 15439545, 23872185, 53763535, 63075321, 41337555, 60923577, 51394665, 56802249, 110691295, 73809496, 89870985, 82771336, 92586585, 150672921, 108212055 (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 Amiram Eldar, Table of n, a(n) for n = 1..276 Jan Munch Pedersen, Tables of Aliquot Cycles. FORMULA The values of n for which isigma(m)=isigma(n)=m+n-1, where n>m and isigma(n) is given by A049417(n). EXAMPLE a(3)=2580105 because 2580105 is the larger member of the third augmented infinitary amicable pair, (2166136,2580105). 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; AugmentedInfinitaryAmicableNumberQ[n_] := If[properinfinitarydivisorsum[properinfinitarydivisorsum[ n] + 1] == n - 1 && ! properinfinitarydivisorsum[n] + 1 == n, True, False]; AugmentedInfinitaryAmicablePairList[k_] := (anlist = Select[Range[k], AugmentedInfinitaryAmicableNumberQ[ # ] &]; prlist = Table[ Sort[{anlist[[n]], properinfinitarydivisorsum[anlist[[n]]] + 1}], {n, 1, Length[anlist]}]; amprlist = Union[prlist, prlist]); data = AugmentedInfinitaryAmicablePairList[10^7]; Table[Last[data[[k]]], {k, 1, Length[data]}] 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] + 1; If[k > n && infs[k] == n - 1, AppendTo[s, k]], {n, 2, 10^9}]; s (* Amiram Eldar, Jan 20 2019 *) CROSSREFS Cf. A126169, A049417, A126168, A037445, A126170, A126171, A126173, A126174, A126176. Sequence in context: A204801 A234837 A233391 * A128837 A297881 A335289 Adjacent sequences: A126172 A126173 A126174 * A126176 A126177 A126178 KEYWORD hard,nonn AUTHOR Ant King, Dec 23 2006 EXTENSIONS a(9)-a(27) from Amiram Eldar, Jan 20 2019 STATUS approved

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Last modified September 22 11:51 EDT 2023. Contains 365531 sequences. (Running on oeis4.)