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 A126172 Smaller element of a reduced infinitary amicable pair. 6
 2024, 62744, 573560, 1000824, 1173704, 1208504, 1921185, 2140215, 2198504, 2312024, 2580864, 4012184, 5416280, 9247095, 12500865, 13496840, 23939685, 26409320, 34093304, 37324584, 40818855, 52026920, 66275384, 76011992, 79842104, 101366342, 101589320, 106004024 (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..278 Jan Munch Pedersen, Tables of Aliquot Cycles. FORMULA The values of m for which isigma(m)=isigma(n)=m+n+1, where m 1, True, False]; ReducedInfinitaryAmicablePairList[k_] := (anlist = Select[Range[k], ReducedInfinitaryAmicableNumberQ[ # ] &]; prlist = Table[Sort[{anlist[[n]], properinfinitarydivisorsum[anlist[[n]]] - 1}], {n, 1, Length[anlist]}]; amprlist = Union[prlist, prlist]); data1 = ReducedInfinitaryAmicablePairList[ 10^7]; Table[First[data1[[k]]], {k, 1, Length[data1]}] 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, n]], {n, 2, 10^5}]; s (* Amiram Eldar, Jan 22 2019 *) CROSSREFS Cf. A126169, A049417, A126168, A037445, A126170, A126171, A126173, A126174, A126175, A126176. Sequence in context: A333057 A156855 A306870 * A183999 A360216 A250811 Adjacent sequences: A126169 A126170 A126171 * A126173 A126174 A126175 KEYWORD nonn AUTHOR Ant King, Dec 23 2006 EXTENSIONS a(15)-a(28) from Amiram Eldar, Jan 22 2019 STATUS approved

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Last modified June 9 14:45 EDT 2023. Contains 363181 sequences. (Running on oeis4.)